3x(x-12)+2x=180

Solution for 3x(x-12)+2x=180 equation:

3x(x-12)+2x=180

We move all terms to the left:

3x(x-12)+2x-(180)=0

We add all the numbers together, and all the variables

2x+3x(x-12)-180=0

We multiply parentheses

3x^2+2x-36x-180=0

We add all the numbers together, and all the variables

3x^2-34x-180=0

a = 3; b = -34; c = -180;
Δ = b2-4ac
Δ = -342-4·3·(-180)
Δ = 3316
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:

$\sqrt{\Delta}=\sqrt{3316}=\sqrt{4*829}=\sqrt{4}*\sqrt{829}=2\sqrt{829}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{829}}{2*3}=\frac{34-2\sqrt{829}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{829}}{2*3}=\frac{34+2\sqrt{829}}{6}
$