(x-10)(x+22)=0

Solution for (x-10)(x+22)=0 equation:

(x-10)(x+22)=0

We multiply parentheses ..

(+x^2+22x-10x-220)=0

We get rid of parentheses

x^2+22x-10x-220=0

We add all the numbers together, and all the variables

x^2+12x-220=0

a = 1; b = 12; c = -220;
Δ = b2-4ac
Δ = 122-4·1·(-220)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-32}{2*1}=\frac{-44}{2}
=-22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+32}{2*1}=\frac{20}{2}
=10
$