x^2+17x+72=180

Solution for x^2+17x+72=180 equation:

x^2+17x+72=180

We move all terms to the left:

x^2+17x+72-(180)=0

We add all the numbers together, and all the variables

x^2+17x-108=0

a = 1; b = 17; c = -108;
Δ = b2-4ac
Δ = 172-4·1·(-108)
Δ = 721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{721}}{2*1}=\frac{-17-\sqrt{721}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{721}}{2*1}=\frac{-17+\sqrt{721}}{2}
$