3x(4x+40)=180

Solution for 3x(4x+40)=180 equation:

3x(4x+40)=180

We move all terms to the left:

3x(4x+40)-(180)=0

We multiply parentheses

12x^2+120x-180=0

a = 12; b = 120; c = -180;
Δ = b2-4ac
Δ = 1202-4·12·(-180)
Δ = 23040
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:

$\sqrt{\Delta}=\sqrt{23040}=\sqrt{2304*10}=\sqrt{2304}*\sqrt{10}=48\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-48\sqrt{10}}{2*12}=\frac{-120-48\sqrt{10}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+48\sqrt{10}}{2*12}=\frac{-120+48\sqrt{10}}{24}
$