76=8x^2+23-9173

Solution for 76=8x^2+23-9173 equation:

76=8x^2+23-9173

We move all terms to the left:

76-(8x^2+23-9173)=0

We get rid of parentheses

-8x^2-23+9173+76=0

We add all the numbers together, and all the variables

-8x^2+9226=0

a = -8; b = 0; c = +9226;
Δ = b2-4ac
Δ = 02-4·(-8)·9226
Δ = 295232
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:

$\sqrt{\Delta}=\sqrt{295232}=\sqrt{64*4613}=\sqrt{64}*\sqrt{4613}=8\sqrt{4613}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{4613}}{2*-8}=\frac{0-8\sqrt{4613}}{-16}
=-\frac{8\sqrt{4613}}{-16}
=-\frac{\sqrt{4613}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{4613}}{2*-8}=\frac{0+8\sqrt{4613}}{-16}
=\frac{8\sqrt{4613}}{-16}
=\frac{\sqrt{4613}}{-2}
$