-5x^2=30x+40

Solution for -5x^2=30x+40 equation:

-5x^2=30x+40

We move all terms to the left:

-5x^2-(30x+40)=0

We get rid of parentheses

-5x^2-30x-40=0

a = -5; b = -30; c = -40;
Δ = b2-4ac
Δ = -302-4·(-5)·(-40)
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*-5}=\frac{20}{-10}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10}{2*-5}=\frac{40}{-10}
=-4
$