0=8x^2+6x-12

Solution for 0=8x^2+6x-12 equation:

0=8x^2+6x-12

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-8x^2-6x+12=0

a = -8; b = -6; c = +12;
Δ = b2-4ac
Δ = -62-4·(-8)·12
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{105}}{2*-8}=\frac{6-2\sqrt{105}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{105}}{2*-8}=\frac{6+2\sqrt{105}}{-16}
$