(6x)(3x+45)=180

Solution for (6x)(3x+45)=180 equation:

(6x)(3x+45)=180

We move all terms to the left:

(6x)(3x+45)-(180)=0

We multiply parentheses

18x^2+270x-180=0

a = 18; b = 270; c = -180;
Δ = b2-4ac
Δ = 2702-4·18·(-180)
Δ = 85860
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:

$\sqrt{\Delta}=\sqrt{85860}=\sqrt{324*265}=\sqrt{324}*\sqrt{265}=18\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(270)-18\sqrt{265}}{2*18}=\frac{-270-18\sqrt{265}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(270)+18\sqrt{265}}{2*18}=\frac{-270+18\sqrt{265}}{36}
$