(X-12)(2x+6)=0

Solution for (X-12)(2x+6)=0 equation:

(X-12)(2X+6)=0

We multiply parentheses ..

(+2X^2+6X-24X-72)=0

We get rid of parentheses

2X^2+6X-24X-72=0

We add all the numbers together, and all the variables

2X^2-18X-72=0

a = 2; b = -18; c = -72;
Δ = b2-4ac
Δ = -182-4·2·(-72)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-30}{2*2}=\frac{-12}{4}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+30}{2*2}=\frac{48}{4}
=12
$