(x+1)(x+1)=69

Solution for (x+1)(x+1)=69 equation:

(x+1)(x+1)=69

We move all terms to the left:

(x+1)(x+1)-(69)=0

We multiply parentheses ..

(+x^2+x+x+1)-69=0

We get rid of parentheses

x^2+x+x+1-69=0

We add all the numbers together, and all the variables

x^2+2x-68=0

a = 1; b = 2; c = -68;
Δ = b2-4ac
Δ = 22-4·1·(-68)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{69}}{2*1}=\frac{-2-2\sqrt{69}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{69}}{2*1}=\frac{-2+2\sqrt{69}}{2}
$