4x^2-28x-31=0

Solution for 4x^2-28x-31=0 equation:

4x^2-28x-31=0

a = 4; b = -28; c = -31;
Δ = b2-4ac
Δ = -282-4·4·(-31)
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-16\sqrt{5}}{2*4}=\frac{28-16\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+16\sqrt{5}}{2*4}=\frac{28+16\sqrt{5}}{8}
$