X^2+29x=-180

Solution for X^2+29x=-180 equation:

X^2+29X=-180

We move all terms to the left:

X^2+29X-(-180)=0

We add all the numbers together, and all the variables

X^2+29X+180=0

a = 1; b = 29; c = +180;
Δ = b2-4ac
Δ = 292-4·1·180
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-11}{2*1}=\frac{-40}{2}
=-20
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+11}{2*1}=\frac{-18}{2}
=-9
$