(x-16)(x-100)=0

Solution for (x-16)(x-100)=0 equation:

(x-16)(x-100)=0

We multiply parentheses ..

(+x^2-100x-16x+1600)=0

We get rid of parentheses

x^2-100x-16x+1600=0

We add all the numbers together, and all the variables

x^2-116x+1600=0

a = 1; b = -116; c = +1600;
Δ = b2-4ac
Δ = -1162-4·1·1600
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-84}{2*1}=\frac{32}{2}
=16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+84}{2*1}=\frac{200}{2}
=100
$