9x+24=3x^2-6

Solution for 9x+24=3x^2-6 equation:

9x+24=3x^2-6

We move all terms to the left:

9x+24-(3x^2-6)=0

We get rid of parentheses

-3x^2+9x+6+24=0

We add all the numbers together, and all the variables

-3x^2+9x+30=0

a = -3; b = 9; c = +30;
Δ = b2-4ac
Δ = 92-4·(-3)·30
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-21}{2*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+21}{2*-3}=\frac{12}{-6}
=-2
$