7x-1+x^2+37=180

Solution for 7x-1+x^2+37=180 equation:

7x-1+x^2+37=180

We move all terms to the left:

7x-1+x^2+37-(180)=0

We add all the numbers together, and all the variables

x^2+7x-144=0

a = 1; b = 7; c = -144;
Δ = b2-4ac
Δ = 72-4·1·(-144)
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{-(7)-25}{2*1}=\frac{-32}{2}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+25}{2*1}=\frac{18}{2}
=9
$