x+23=x^2-43

Solution for x+23=x^2-43 equation:

x+23=x^2-43

We move all terms to the left:

x+23-(x^2-43)=0

We get rid of parentheses

-x^2+x+43+23=0

We add all the numbers together, and all the variables

-1x^2+x+66=0

a = -1; b = 1; c = +66;
Δ = b2-4ac
Δ = 12-4·(-1)·66
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{265}}{2*-1}=\frac{-1-\sqrt{265}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{265}}{2*-1}=\frac{-1+\sqrt{265}}{-2}
$