2x^2-90=-8x

Solution for 2x^2-90=-8x equation:

2x^2-90=-8x

We move all terms to the left:

2x^2-90-(-8x)=0

We get rid of parentheses

2x^2+8x-90=0

a = 2; b = 8; c = -90;
Δ = b2-4ac
Δ = 82-4·2·(-90)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-28}{2*2}=\frac{-36}{4}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+28}{2*2}=\frac{20}{4}
=5
$