(x)2-(x+1)2=103

Solution for (x)2-(x+1)2=103 equation:

(x)2-(x+1)2=103

We move all terms to the left:

(x)2-(x+1)2-(103)=0

We add all the numbers together, and all the variables

x^2-(x+1)2-103=0

We multiply parentheses

x^2-2x-2-103=0

We add all the numbers together, and all the variables

x^2-2x-105=0

a = 1; b = -2; c = -105;
Δ = b2-4ac
Δ = -22-4·1·(-105)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{106}}{2*1}=\frac{2-2\sqrt{106}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{106}}{2*1}=\frac{2+2\sqrt{106}}{2}
$