24=6x^2+6x-36

Solution for 24=6x^2+6x-36 equation:

24=6x^2+6x-36

We move all terms to the left:

24-(6x^2+6x-36)=0

We get rid of parentheses

-6x^2-6x+36+24=0

We add all the numbers together, and all the variables

-6x^2-6x+60=0

a = -6; b = -6; c = +60;
Δ = b2-4ac
Δ = -62-4·(-6)·60
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{41}}{2*-6}=\frac{6-6\sqrt{41}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{41}}{2*-6}=\frac{6+6\sqrt{41}}{-12}
$