x^2+18x+140=180

Solution for x^2+18x+140=180 equation:

x^2+18x+140=180

We move all terms to the left:

x^2+18x+140-(180)=0

We add all the numbers together, and all the variables

x^2+18x-40=0

a = 1; b = 18; c = -40;
Δ = b2-4ac
Δ = 182-4·1·(-40)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-22}{2*1}=\frac{-40}{2}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+22}{2*1}=\frac{4}{2}
=2
$