(3x-48)(9x)=180

Solution for (3x-48)(9x)=180 equation:

(3x-48)(9x)=180

We move all terms to the left:

(3x-48)(9x)-(180)=0

We multiply parentheses

27x^2-432x-180=0

a = 27; b = -432; c = -180;
Δ = b2-4ac
Δ = -4322-4·27·(-180)
Δ = 206064
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:

$\sqrt{\Delta}=\sqrt{206064}=\sqrt{1296*159}=\sqrt{1296}*\sqrt{159}=36\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-432)-36\sqrt{159}}{2*27}=\frac{432-36\sqrt{159}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-432)+36\sqrt{159}}{2*27}=\frac{432+36\sqrt{159}}{54}
$