-9=8x^2+31x

Solution for -9=8x^2+31x equation:

-9=8x^2+31x

We move all terms to the left:

-9-(8x^2+31x)=0

We get rid of parentheses

-8x^2-31x-9=0

a = -8; b = -31; c = -9;
Δ = b2-4ac
Δ = -312-4·(-8)·(-9)
Δ = 673
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{673}}{2*-8}=\frac{31-\sqrt{673}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{673}}{2*-8}=\frac{31+\sqrt{673}}{-16}
$