x^2+18x+80=3

Solution for x^2+18x+80=3 equation:

x^2+18x+80=3

We move all terms to the left:

x^2+18x+80-(3)=0

We add all the numbers together, and all the variables

x^2+18x+77=0

a = 1; b = 18; c = +77;
Δ = b2-4ac
Δ = 182-4·1·77
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4}{2*1}=\frac{-22}{2}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4}{2*1}=\frac{-14}{2}
=-7
$