(4x+12)(15x-3)=180

Solution for (4x+12)(15x-3)=180 equation:

(4x+12)(15x-3)=180

We move all terms to the left:

(4x+12)(15x-3)-(180)=0

We multiply parentheses ..

(+60x^2-12x+180x-36)-180=0

We get rid of parentheses

60x^2-12x+180x-36-180=0

We add all the numbers together, and all the variables

60x^2+168x-216=0

a = 60; b = 168; c = -216;
Δ = b2-4ac
Δ = 1682-4·60·(-216)
Δ = 80064
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:

$\sqrt{\Delta}=\sqrt{80064}=\sqrt{576*139}=\sqrt{576}*\sqrt{139}=24\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-24\sqrt{139}}{2*60}=\frac{-168-24\sqrt{139}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+24\sqrt{139}}{2*60}=\frac{-168+24\sqrt{139}}{120}
$