3x(x+1)=24

Solution for 3x(x+1)=24 equation:

3x(x+1)=24

We move all terms to the left:

3x(x+1)-(24)=0

We multiply parentheses

3x^2+3x-24=0

a = 3; b = 3; c = -24;
Δ = b2-4ac
Δ = 32-4·3·(-24)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{33}}{2*3}=\frac{-3-3\sqrt{33}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{33}}{2*3}=\frac{-3+3\sqrt{33}}{6}
$