x^2+2x+2=9802

Solution for x^2+2x+2=9802 equation:

x^2+2x+2=9802

We move all terms to the left:

x^2+2x+2-(9802)=0

We add all the numbers together, and all the variables

x^2+2x-9800=0

a = 1; b = 2; c = -9800;
Δ = b2-4ac
Δ = 22-4·1·(-9800)
Δ = 39204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39204}=198$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-198}{2*1}=\frac{-200}{2}
=-100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+198}{2*1}=\frac{196}{2}
=98
$