(3x-9)(x+15)(90)=180

Solution for (3x-9)(x+15)(90)=180 equation:

(3x-9)(x+15)(90)=180

We move all terms to the left:

(3x-9)(x+15)(90)-(180)=0

We multiply parentheses ..

(+3x^2+45x-9x-135)90-180=0

We multiply parentheses

270x^2+4050x-810x-12150-180=0

We add all the numbers together, and all the variables

270x^2+3240x-12330=0

a = 270; b = 3240; c = -12330;
Δ = b2-4ac
Δ = 32402-4·270·(-12330)
Δ = 23814000
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:

$\sqrt{\Delta}=\sqrt{23814000}=\sqrt{1587600*15}=\sqrt{1587600}*\sqrt{15}=1260\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3240)-1260\sqrt{15}}{2*270}=\frac{-3240-1260\sqrt{15}}{540}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3240)+1260\sqrt{15}}{2*270}=\frac{-3240+1260\sqrt{15}}{540}
$