12x(x-5)=108

Solution for 12x(x-5)=108 equation:

12x(x-5)=108

We move all terms to the left:

12x(x-5)-(108)=0

We multiply parentheses

12x^2-60x-108=0

a = 12; b = -60; c = -108;
Δ = b2-4ac
Δ = -602-4·12·(-108)
Δ = 8784
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:

$\sqrt{\Delta}=\sqrt{8784}=\sqrt{144*61}=\sqrt{144}*\sqrt{61}=12\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-12\sqrt{61}}{2*12}=\frac{60-12\sqrt{61}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+12\sqrt{61}}{2*12}=\frac{60+12\sqrt{61}}{24}
$