(X-12)(x-7)=0

Solution for (X-12)(x-7)=0 equation:

(X-12)(X-7)=0

We multiply parentheses ..

(+X^2-7X-12X+84)=0

We get rid of parentheses

X^2-7X-12X+84=0

We add all the numbers together, and all the variables

X^2-19X+84=0

a = 1; b = -19; c = +84;
Δ = b2-4ac
Δ = -192-4·1·84
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-5}{2*1}=\frac{14}{2}
=7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+5}{2*1}=\frac{24}{2}
=12
$