x^2+17x+72=132

Solution for x^2+17x+72=132 equation:

x^2+17x+72=132

We move all terms to the left:

x^2+17x+72-(132)=0

We add all the numbers together, and all the variables

x^2+17x-60=0

a = 1; b = 17; c = -60;
Δ = b2-4ac
Δ = 172-4·1·(-60)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-23}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+23}{2*1}=\frac{6}{2}
=3
$