(x+1)(x+1)+2=102

Solution for (x+1)(x+1)+2=102 equation:

(x+1)(x+1)+2=102

We move all terms to the left:

(x+1)(x+1)+2-(102)=0

We add all the numbers together, and all the variables

(x+1)(x+1)-100=0

We multiply parentheses ..

(+x^2+x+x+1)-100=0

We get rid of parentheses

x^2+x+x+1-100=0

We add all the numbers together, and all the variables

x^2+2x-99=0

a = 1; b = 2; c = -99;
Δ = b2-4ac
Δ = 22-4·1·(-99)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-20}{2*1}=\frac{-22}{2}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+20}{2*1}=\frac{18}{2}
=9
$