x^2-24+5x=180

Solution for x^2-24+5x=180 equation:

x^2-24+5x=180

We move all terms to the left:

x^2-24+5x-(180)=0

We add all the numbers together, and all the variables

x^2+5x-204=0

a = 1; b = 5; c = -204;
Δ = b2-4ac
Δ = 52-4·1·(-204)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-29}{2*1}=\frac{-34}{2}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+29}{2*1}=\frac{24}{2}
=12
$