6x(15x+75)=180

Solution for 6x(15x+75)=180 equation:

6x(15x+75)=180

We move all terms to the left:

6x(15x+75)-(180)=0

We multiply parentheses

90x^2+450x-180=0

a = 90; b = 450; c = -180;
Δ = b2-4ac
Δ = 4502-4·90·(-180)
Δ = 267300
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:

$\sqrt{\Delta}=\sqrt{267300}=\sqrt{8100*33}=\sqrt{8100}*\sqrt{33}=90\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(450)-90\sqrt{33}}{2*90}=\frac{-450-90\sqrt{33}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(450)+90\sqrt{33}}{2*90}=\frac{-450+90\sqrt{33}}{180}
$