x^2-23x=23

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

x^2-23x=23

We move all terms to the left:

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

a = 1; b = -23; c = -23;
Δ = b2-4ac
Δ = -232-4·1·(-23)
Δ = 621
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:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-3\sqrt{69}}{2*1}=\frac{23-3\sqrt{69}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+3\sqrt{69}}{2*1}=\frac{23+3\sqrt{69}}{2}
$