X2+2x+1=80

Solution for X2+2x+1=80 equation:

X2+2X+1=80

We move all terms to the left:

X2+2X+1-(80)=0

We add all the numbers together, and all the variables

X^2+2X-79=0

a = 1; b = 2; c = -79;
Δ = b2-4ac
Δ = 22-4·1·(-79)
Δ = 320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8\sqrt{5}}{2*1}=\frac{-2-8\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8\sqrt{5}}{2*1}=\frac{-2+8\sqrt{5}}{2}
$