23x-x^2=130

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

23x-x^2=130

We move all terms to the left:

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

We add all the numbers together, and all the variables

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