(x-12)(x-5)=44

Solution for (x-12)(x-5)=44 equation:

(x-12)(x-5)=44

We move all terms to the left:

(x-12)(x-5)-(44)=0

We multiply parentheses ..

(+x^2-5x-12x+60)-44=0

We get rid of parentheses

x^2-5x-12x+60-44=0

We add all the numbers together, and all the variables

x^2-17x+16=0

a = 1; b = -17; c = +16;
Δ = b2-4ac
Δ = -172-4·1·16
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-15}{2*1}=\frac{2}{2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+15}{2*1}=\frac{32}{2}
=16
$