24=3x^2+2x

Solution for 24=3x^2+2x equation:

24=3x^2+2x

We move all terms to the left:

24-(3x^2+2x)=0

We get rid of parentheses

-3x^2-2x+24=0

a = -3; b = -2; c = +24;
Δ = b2-4ac
Δ = -22-4·(-3)·24
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{73}}{2*-3}=\frac{2-2\sqrt{73}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{73}}{2*-3}=\frac{2+2\sqrt{73}}{-6}
$