-8x+23=x^2

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

-8x+23=x^2

We move all terms to the left:

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

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

We add all the numbers together, and all the variables

-1x^2-8x+23=0

a = -1; b = -8; c = +23;
Δ = b2-4ac
Δ = -82-4·(-1)·23
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{39}}{2*-1}=\frac{8-2\sqrt{39}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{39}}{2*-1}=\frac{8+2\sqrt{39}}{-2}
$