x^2=11x-23

Solution for x^2=11x-23 equation:

x^2=11x-23

We move all terms to the left:

x^2-(11x-23)=0

We get rid of parentheses

x^2-11x+23=0

a = 1; b = -11; c = +23;
Δ = b2-4ac
Δ = -112-4·1·23
Δ = 29
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{-(-11)-\sqrt{29}}{2*1}=\frac{11-\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{29}}{2*1}=\frac{11+\sqrt{29}}{2}
$