120+40x(x-12)=30x

Solution for 120+40x(x-12)=30x equation:

120+40x(x-12)=30x

We move all terms to the left:

120+40x(x-12)-(30x)=0

We add all the numbers together, and all the variables

-30x+40x(x-12)+120=0

We multiply parentheses

40x^2-30x-480x+120=0

We add all the numbers together, and all the variables

40x^2-510x+120=0

a = 40; b = -510; c = +120;
Δ = b2-4ac
Δ = -5102-4·40·120
Δ = 240900
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:

$\sqrt{\Delta}=\sqrt{240900}=\sqrt{100*2409}=\sqrt{100}*\sqrt{2409}=10\sqrt{2409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-510)-10\sqrt{2409}}{2*40}=\frac{510-10\sqrt{2409}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-510)+10\sqrt{2409}}{2*40}=\frac{510+10\sqrt{2409}}{80}
$