-8=2x^2+9x

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

-8=2x^2+9x

We move all terms to the left:

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

We get rid of parentheses

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

a = -2; b = -9; c = -8;
Δ = b2-4ac
Δ = -92-4·(-2)·(-8)
Δ = 17
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{-(-9)-\sqrt{17}}{2*-2}=\frac{9-\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{17}}{2*-2}=\frac{9+\sqrt{17}}{-4}
$