X^2-x+24+2x=180

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

X^2-X+24+2X=180

We move all terms to the left:

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

We add all the numbers together, and all the variables

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