12x(10x+20)=180

Solution for 12x(10x+20)=180 equation:

12x(10x+20)=180

We move all terms to the left:

12x(10x+20)-(180)=0

We multiply parentheses

120x^2+240x-180=0

a = 120; b = 240; c = -180;
Δ = b2-4ac
Δ = 2402-4·120·(-180)
Δ = 144000
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:

$\sqrt{\Delta}=\sqrt{144000}=\sqrt{14400*10}=\sqrt{14400}*\sqrt{10}=120\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-120\sqrt{10}}{2*120}=\frac{-240-120\sqrt{10}}{240}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+120\sqrt{10}}{2*120}=\frac{-240+120\sqrt{10}}{240}
$