x^2-23x=-130

Solution for x^2-23x=-130 equation:

x^2-23x=-130

We move all terms to the left:

x^2-23x-(-130)=0

We add all the numbers together, and all the variables

x^2-23x+130=0

a = 1; b = -23; c = +130;
Δ = b2-4ac
Δ = -232-4·1·130
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-3}{2*1}=\frac{20}{2}
=10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+3}{2*1}=\frac{26}{2}
=13
$