8x^2-2=24

Solution for 8x^2-2=24 equation:

8x^2-2=24

We move all terms to the left:

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

We add all the numbers together, and all the variables

8x^2-26=0

a = 8; b = 0; c = -26;
Δ = b2-4ac
Δ = 02-4·8·(-26)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{13}}{2*8}=\frac{0-8\sqrt{13}}{16}
=-\frac{8\sqrt{13}}{16}
=-\frac{\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{13}}{2*8}=\frac{0+8\sqrt{13}}{16}
=\frac{8\sqrt{13}}{16}
=\frac{\sqrt{13}}{2}
$