x2+x=80

Solution for x2+x=80 equation:

x2+x=80

We move all terms to the left:

x2+x-(80)=0

We add all the numbers together, and all the variables

x^2+x-80=0

a = 1; b = 1; c = -80;
Δ = b2-4ac
Δ = 12-4·1·(-80)
Δ = 321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{321}}{2*1}=\frac{-1-\sqrt{321}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{321}}{2*1}=\frac{-1+\sqrt{321}}{2}
$