(9x-45)6x=180

Solution for (9x-45)6x=180 equation:

(9x-45)6x=180

We move all terms to the left:

(9x-45)6x-(180)=0

We multiply parentheses

54x^2-270x-180=0

a = 54; b = -270; c = -180;
Δ = b2-4ac
Δ = -2702-4·54·(-180)
Δ = 111780
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:

$\sqrt{\Delta}=\sqrt{111780}=\sqrt{324*345}=\sqrt{324}*\sqrt{345}=18\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-18\sqrt{345}}{2*54}=\frac{270-18\sqrt{345}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+18\sqrt{345}}{2*54}=\frac{270+18\sqrt{345}}{108}
$