12x(x+10)=24

Solution for 12x(x+10)=24 equation:

12x(x+10)=24

We move all terms to the left:

12x(x+10)-(24)=0

We multiply parentheses

12x^2+120x-24=0

a = 12; b = 120; c = -24;
Δ = b2-4ac
Δ = 1202-4·12·(-24)
Δ = 15552
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:

$\sqrt{\Delta}=\sqrt{15552}=\sqrt{5184*3}=\sqrt{5184}*\sqrt{3}=72\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-72\sqrt{3}}{2*12}=\frac{-120-72\sqrt{3}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+72\sqrt{3}}{2*12}=\frac{-120+72\sqrt{3}}{24}
$