8x2-6x-12=24

Solution for 8x2-6x-12=24 equation:

8x^2-6x-12=24

We move all terms to the left:

8x^2-6x-12-(24)=0

We add all the numbers together, and all the variables

8x^2-6x-36=0

a = 8; b = -6; c = -36;
Δ = b2-4ac
Δ = -62-4·8·(-36)
Δ = 1188
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:

$\sqrt{\Delta}=\sqrt{1188}=\sqrt{36*33}=\sqrt{36}*\sqrt{33}=6\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{33}}{2*8}=\frac{6-6\sqrt{33}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{33}}{2*8}=\frac{6+6\sqrt{33}}{16}
$