8x^2=23

Solution for 8x^2=23 equation:

8x^2=23

We move all terms to the left:

8x^2-(23)=0

a = 8; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·8·(-23)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{46}}{2*8}=\frac{0-4\sqrt{46}}{16}
=-\frac{4\sqrt{46}}{16}
=-\frac{\sqrt{46}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{46}}{2*8}=\frac{0+4\sqrt{46}}{16}
=\frac{4\sqrt{46}}{16}
=\frac{\sqrt{46}}{4}
$