33(9x-3)6x=180

Solution for 33(9x-3)6x=180 equation:

33(9x-3)6x=180

We move all terms to the left:

33(9x-3)6x-(180)=0

We multiply parentheses

1782x^2-594x-180=0

a = 1782; b = -594; c = -180;
Δ = b2-4ac
Δ = -5942-4·1782·(-180)
Δ = 1635876
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:

$\sqrt{\Delta}=\sqrt{1635876}=\sqrt{2916*561}=\sqrt{2916}*\sqrt{561}=54\sqrt{561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-594)-54\sqrt{561}}{2*1782}=\frac{594-54\sqrt{561}}{3564}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-594)+54\sqrt{561}}{2*1782}=\frac{594+54\sqrt{561}}{3564}
$