4x^2+36x+31=0

Solution for 4x^2+36x+31=0 equation:

4x^2+36x+31=0

a = 4; b = 36; c = +31;
Δ = b2-4ac
Δ = 362-4·4·31
Δ = 800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-20\sqrt{2}}{2*4}=\frac{-36-20\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+20\sqrt{2}}{2*4}=\frac{-36+20\sqrt{2}}{8}
$