x^2=23x-60

Solution for x^2=23x-60 equation:

x^2=23x-60

We move all terms to the left:

x^2-(23x-60)=0

We get rid of parentheses

x^2-23x+60=0

a = 1; b = -23; c = +60;
Δ = b2-4ac
Δ = -232-4·1·60
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-17}{2*1}=\frac{6}{2}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+17}{2*1}=\frac{40}{2}
=20
$