(x-24)x+23=180

Solution for (x-24)x+23=180 equation:

(x-24)x+23=180

We move all terms to the left:

(x-24)x+23-(180)=0

We add all the numbers together, and all the variables

(x-24)x-157=0

We multiply parentheses

x^2-24x-157=0

a = 1; b = -24; c = -157;
Δ = b2-4ac
Δ = -242-4·1·(-157)
Δ = 1204
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:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{301}}{2*1}=\frac{24-2\sqrt{301}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{301}}{2*1}=\frac{24+2\sqrt{301}}{2}
$