(x-100)(x+1)=0

Solution for (x-100)(x+1)=0 equation:

(x-100)(x+1)=0

We multiply parentheses ..

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

We get rid of parentheses

x^2+x-100x-100=0

We add all the numbers together, and all the variables

x^2-99x-100=0

a = 1; b = -99; c = -100;
Δ = b2-4ac
Δ = -992-4·1·(-100)
Δ = 10201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10201}=101$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-101}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+101}{2*1}=\frac{200}{2}
=100
$