x^2+3x-24=12

Solution for x^2+3x-24=12 equation:

x^2+3x-24=12

We move all terms to the left:

x^2+3x-24-(12)=0

We add all the numbers together, and all the variables

x^2+3x-36=0

a = 1; b = 3; c = -36;
Δ = b2-4ac
Δ = 32-4·1·(-36)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{17}}{2*1}=\frac{-3-3\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{17}}{2*1}=\frac{-3+3\sqrt{17}}{2}
$