(5x)(6x-9)=180

Solution for (5x)(6x-9)=180 equation:

(5x)(6x-9)=180

We move all terms to the left:

(5x)(6x-9)-(180)=0

We multiply parentheses

30x^2-45x-180=0

a = 30; b = -45; c = -180;
Δ = b2-4ac
Δ = -452-4·30·(-180)
Δ = 23625
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:

$\sqrt{\Delta}=\sqrt{23625}=\sqrt{225*105}=\sqrt{225}*\sqrt{105}=15\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-15\sqrt{105}}{2*30}=\frac{45-15\sqrt{105}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+15\sqrt{105}}{2*30}=\frac{45+15\sqrt{105}}{60}
$