-8=2x^2+30x

Solution for -8=2x^2+30x equation:

-8=2x^2+30x

We move all terms to the left:

-8-(2x^2+30x)=0

We get rid of parentheses

-2x^2-30x-8=0

a = -2; b = -30; c = -8;
Δ = b2-4ac
Δ = -302-4·(-2)·(-8)
Δ = 836
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:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{209}}{2*-2}=\frac{30-2\sqrt{209}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{209}}{2*-2}=\frac{30+2\sqrt{209}}{-4}
$