-8x^2-6=-102

Solution for -8x^2-6=-102 equation:

-8x^2-6=-102

We move all terms to the left:

-8x^2-6-(-102)=0

We add all the numbers together, and all the variables

-8x^2+96=0

a = -8; b = 0; c = +96;
Δ = b2-4ac
Δ = 02-4·(-8)·96
Δ = 3072
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:

$\sqrt{\Delta}=\sqrt{3072}=\sqrt{1024*3}=\sqrt{1024}*\sqrt{3}=32\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{3}}{2*-8}=\frac{0-32\sqrt{3}}{-16}
=-\frac{32\sqrt{3}}{-16}
=-\frac{2\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{3}}{2*-8}=\frac{0+32\sqrt{3}}{-16}
=\frac{32\sqrt{3}}{-16}
=\frac{2\sqrt{3}}{-1}
$