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

Solution for (X-5)(x-12)=0 equation:

(X-5)(X-12)=0

We multiply parentheses ..

(+X^2-12X-5X+60)=0

We get rid of parentheses

X^2-12X-5X+60=0

We add all the numbers together, and all the variables

X^2-17X+60=0

a = 1; b = -17; c = +60;
Δ = b2-4ac
Δ = -172-4·1·60
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-7}{2*1}=\frac{10}{2}
=5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+7}{2*1}=\frac{24}{2}
=12
$