import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem mathd_algebra_116 (k x : ℝ) (h₀ : x = (13 - Real.sqrt 131) / 4)
    (h₁ : 2 * x ^ 2 - 13 * x + k = 0) : k = 19 / 4 := by sorry