x^2+9x+44=180

Solution for x^2+9x+44=180 equation:

x^2+9x+44=180

We move all terms to the left:

x^2+9x+44-(180)=0

We add all the numbers together, and all the variables

x^2+9x-136=0

a = 1; b = 9; c = -136;
Δ = b2-4ac
Δ = 92-4·1·(-136)
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{-(9)-25}{2*1}=\frac{-34}{2}
=-17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+25}{2*1}=\frac{16}{2}
=8
$