8x^2+5x-31=0

Solution for 8x^2+5x-31=0 equation:

8x^2+5x-31=0

a = 8; b = 5; c = -31;
Δ = b2-4ac
Δ = 52-4·8·(-31)
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{113}}{2*8}=\frac{-5-3\sqrt{113}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{113}}{2*8}=\frac{-5+3\sqrt{113}}{16}
$