(x-10)(x-1)=22

Solution for (x-10)(x-1)=22 equation:

(x-10)(x-1)=22

We move all terms to the left:

(x-10)(x-1)-(22)=0

We multiply parentheses ..

(+x^2-1x-10x+10)-22=0

We get rid of parentheses

x^2-1x-10x+10-22=0

We add all the numbers together, and all the variables

x^2-11x-12=0

a = 1; b = -11; c = -12;
Δ = b2-4ac
Δ = -112-4·1·(-12)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-13}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+13}{2*1}=\frac{24}{2}
=12
$