6x(9x-27)=180

Solution for 6x(9x-27)=180 equation:

6x(9x-27)=180

We move all terms to the left:

6x(9x-27)-(180)=0

We multiply parentheses

54x^2-162x-180=0

a = 54; b = -162; c = -180;
Δ = b2-4ac
Δ = -1622-4·54·(-180)
Δ = 65124
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:

$\sqrt{\Delta}=\sqrt{65124}=\sqrt{324*201}=\sqrt{324}*\sqrt{201}=18\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-18\sqrt{201}}{2*54}=\frac{162-18\sqrt{201}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+18\sqrt{201}}{2*54}=\frac{162+18\sqrt{201}}{108}
$