x^2=-25x-100

Solution for x^2=-25x-100 equation:

x^2=-25x-100

We move all terms to the left:

x^2-(-25x-100)=0

We get rid of parentheses

x^2+25x+100=0

a = 1; b = 25; c = +100;
Δ = b2-4ac
Δ = 252-4·1·100
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-15}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+15}{2*1}=\frac{-10}{2}
=-5
$