(X-10)*(x-6)=32

Solution for (X-10)*(x-6)=32 equation:

(X-10)(X-6)=32

We move all terms to the left:

(X-10)(X-6)-(32)=0

We multiply parentheses ..

(+X^2-6X-10X+60)-32=0

We get rid of parentheses

X^2-6X-10X+60-32=0

We add all the numbers together, and all the variables

X^2-16X+28=0

a = 1; b = -16; c = +28;
Δ = b2-4ac
Δ = -162-4·1·28
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12}{2*1}=\frac{4}{2}
=2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12}{2*1}=\frac{28}{2}
=14
$