x^2-x+24=180

Solution for x^2-x+24=180 equation:

x^2-x+24=180

We move all terms to the left:

x^2-x+24-(180)=0

We add all the numbers together, and all the variables

x^2-1x-156=0

a = 1; b = -1; c = -156;
Δ = b2-4ac
Δ = -12-4·1·(-156)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-25}{2*1}=\frac{-24}{2}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+25}{2*1}=\frac{26}{2}
=13
$