8x^2+12=102

Solution for 8x^2+12=102 equation:

8x^2+12=102

We move all terms to the left:

8x^2+12-(102)=0

We add all the numbers together, and all the variables

8x^2-90=0

a = 8; b = 0; c = -90;
Δ = b2-4ac
Δ = 02-4·8·(-90)
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{5}}{2*8}=\frac{0-24\sqrt{5}}{16}
=-\frac{24\sqrt{5}}{16}
=-\frac{3\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{5}}{2*8}=\frac{0+24\sqrt{5}}{16}
=\frac{24\sqrt{5}}{16}
=\frac{3\sqrt{5}}{2}
$