Q:

How do I update the text inside a textblock everytime I enter something in a textbox? 

I now have a WPF app which gives me the result I wanted.  It reads the texts inside the three textboxes "aValue", "bValue" and "cValue" and use those to print a quadratic equation inside the TextBlock "quadEqn".  The problem is that I need the textblock to display or update the equation the moment a number is entered inside any of the textboxes. 
Here's my xaml
<Grid>
    <TextBox x:Name="aValue" KeyDown="TextBox_KeyDown" Text="" .../>
    <TextBox x:Name="bValue" KeyDown="TextBox_KeyDown" Text="" .../>
    <TextBox x:Name="cValue" KeyDown="TextBox_KeyDown" Text="" .../>

        <TextBlock x:Name="quadEqn" Text="" .../>
</Grid>

and the code behind
    private void TextBox_KeyDown(object sender, RoutedEventArgs e)
    {
        sendValuesToEqn();
    }

    public void sendValuesToEqn()
    {
        double a, b, c;
        if(aValue. Text=="") a = 0;
        else a = double. Parse(aValue. Text);

        if (bValue. Text == "") b = 0;
        else b = double. Parse(bValue. Text);

        if (cValue. Text == "") c = 0;
        else c = double. Parse(cValue. Text);

        writeEquation(a, b, c);
    }

    public void writeEquation(double a, double b, double c)
    {
        if(a==0)
        {
            if(b==0)
            {
                if(c==0)
                {
                    quadEqn. Text = "";
                }
                else
                {
                    quadEqn. Text = c.ToString();
                }
            }
            else
            {
                if(c==0)
                {
                    quadEqn. Text = b + "x";
                }
                else
                {
                    quadEqn. Text = b + "x + " + c;
                }
            }
        }
        else
        {
            if(b==0)
            {
                if(c==0)
                {
                    quadEqn. Text = a + "x\xB2";
                }
                else
                {
                    quadEqn. Text = a + "x\xB2 + " + c;
                }
            }
            else
            {
                if(c==0)
                {
                    quadEqn. Text = a + "x\xB2 + " + b + "x";
                }
                else
                {
                    quadEqn. Text = a + "x\xB2 + " + b + "x + " + c;
                }
            }
        }
    }

A:

I believe the best solution is to imlement described logic via MVVM rather than via code behind. 
In your view model you should create three string properties for each TextBox:
public string A { get { ... } set { ... } }
public string B { get { ... } set { ... } }
public string C { get { ... } set { ... } }

Then bind Text property of TextBox'es to these properties.  Don't forget to implement INotifyPropertyChanged in view-model class and to fire PropertyChanged in setters of the view-model properties. 
Then create a property for the equation TextBlock:
public string Equation { get { ... } set { ... } }

Also fire PropertyChanged in setter of this property.  Bind Text property of the equation TextBlock to it. 
In setters of A, B, C call a method which will take these three values and will construct an equation.  When the equation constructed set it to the Equation property of the view-model. 
To change equation immidiately as you typing at TextBox'es in their bindings set UpdateSourceTrigger=PropertyChanged.