3x(4x+6)=24

Solution for 3x(4x+6)=24 equation:

3x(4x+6)=24

We move all terms to the left:

3x(4x+6)-(24)=0

We multiply parentheses

12x^2+18x-24=0

a = 12; b = 18; c = -24;
Δ = b2-4ac
Δ = 182-4·12·(-24)
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{41}}{2*12}=\frac{-18-6\sqrt{41}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{41}}{2*12}=\frac{-18+6\sqrt{41}}{24}
$