24=6x+3x^2

Solution for 24=6x+3x^2 equation:

24=6x+3x^2

We move all terms to the left:

24-(6x+3x^2)=0

We get rid of parentheses

-3x^2-6x+24=0

a = -3; b = -6; c = +24;
Δ = b2-4ac
Δ = -62-4·(-3)·24
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*-3}=\frac{-12}{-6}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*-3}=\frac{24}{-6}
=-4
$