3x(x-12)=4x-36

Solution for 3x(x-12)=4x-36 equation:

3x(x-12)=4x-36

We move all terms to the left:

3x(x-12)-(4x-36)=0

We multiply parentheses

3x^2-36x-(4x-36)=0

We get rid of parentheses

3x^2-36x-4x+36=0

We add all the numbers together, and all the variables

3x^2-40x+36=0

a = 3; b = -40; c = +36;
Δ = b2-4ac
Δ = -402-4·3·36
Δ = 1168
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{73}}{2*3}=\frac{40-4\sqrt{73}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{73}}{2*3}=\frac{40+4\sqrt{73}}{6}
$