X^2-126=2x+1

Solution for X^2-126=2x+1 equation:

X^2-126=2X+1

We move all terms to the left:

X^2-126-(2X+1)=0

We get rid of parentheses

X^2-2X-1-126=0

We add all the numbers together, and all the variables

X^2-2X-127=0

a = 1; b = -2; c = -127;
Δ = b2-4ac
Δ = -22-4·1·(-127)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-16\sqrt{2}}{2*1}=\frac{2-16\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+16\sqrt{2}}{2*1}=\frac{2+16\sqrt{2}}{2}
$