Question: how to solve quadratic equation of degree 4?
Answer: Could you change the title to "Is there a general formula for solving 4th degree polynomial equations" or "Is there a general formula for solving quartic equations?" ... 
Put a*x^4+b*x^3+c*x^2+d*x +e = 0 in wolfram alpha (wolframalpha.com) and then sit back and watch the fireworks!