(3x-2)(x-12)=0

Solution for (3x-2)(x-12)=0 equation:

(3x-2)(x-12)=0

We multiply parentheses ..

(+3x^2-36x-2x+24)=0

We get rid of parentheses

3x^2-36x-2x+24=0

We add all the numbers together, and all the variables

3x^2-38x+24=0

a = 3; b = -38; c = +24;
Δ = b2-4ac
Δ = -382-4·3·24
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-34}{2*3}=\frac{4}{6}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+34}{2*3}=\frac{72}{6}
=12
$