-2x^2=30x+100

Solution for -2x^2=30x+100 equation:

-2x^2=30x+100

We move all terms to the left:

-2x^2-(30x+100)=0

We get rid of parentheses

-2x^2-30x-100=0

a = -2; b = -30; c = -100;
Δ = b2-4ac
Δ = -302-4·(-2)·(-100)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10}{2*-2}=\frac{20}{-4}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10}{2*-2}=\frac{40}{-4}
=-10
$