100x^2+600x=-500

Solution for 100x^2+600x=-500 equation:

100x^2+600x=-500

We move all terms to the left:

100x^2+600x-(-500)=0

We add all the numbers together, and all the variables

100x^2+600x+500=0

a = 100; b = 600; c = +500;
Δ = b2-4ac
Δ = 6002-4·100·500
Δ = 160000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{160000}=400$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(600)-400}{2*100}=\frac{-1000}{200}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(600)+400}{2*100}=\frac{-200}{200}
=-1
$