(60x+180)(15x+5)=180

Solution for (60x+180)(15x+5)=180 equation:

(60x+180)(15x+5)=180

We move all terms to the left:

(60x+180)(15x+5)-(180)=0

We multiply parentheses ..

(+900x^2+300x+2700x+900)-180=0

We get rid of parentheses

900x^2+300x+2700x+900-180=0

We add all the numbers together, and all the variables

900x^2+3000x+720=0

a = 900; b = 3000; c = +720;
Δ = b2-4ac
Δ = 30002-4·900·720
Δ = 6408000
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:

$\sqrt{\Delta}=\sqrt{6408000}=\sqrt{14400*445}=\sqrt{14400}*\sqrt{445}=120\sqrt{445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3000)-120\sqrt{445}}{2*900}=\frac{-3000-120\sqrt{445}}{1800}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3000)+120\sqrt{445}}{2*900}=\frac{-3000+120\sqrt{445}}{1800}
$