23=8x2+3^2=23-8x2+9

Solution for 23=8x2+3^2=23-8x2+9 equation:

23=8x^2+3^2=23-8x^2+9

We move all terms to the left:

23-(8x^2+3^2)=0

We get rid of parentheses

-8x^2+23-3^2=0

We add all the numbers together, and all the variables

-8x^2+14=0

a = -8; b = 0; c = +14;
Δ = b2-4ac
Δ = 02-4·(-8)·14
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{7}}{2*-8}=\frac{0-8\sqrt{7}}{-16}
=-\frac{8\sqrt{7}}{-16}
=-\frac{\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{7}}{2*-8}=\frac{0+8\sqrt{7}}{-16}
=\frac{8\sqrt{7}}{-16}
=\frac{\sqrt{7}}{-2}
$