x2-(x-1)2=159

Solution for x2-(x-1)2=159 equation:

x2-(x-1)2=159

We move all terms to the left:

x2-(x-1)2-(159)=0

We add all the numbers together, and all the variables

x^2-(x-1)2-159=0

We multiply parentheses

x^2-2x+2-159=0

We add all the numbers together, and all the variables

x^2-2x-157=0

a = 1; b = -2; c = -157;
Δ = b2-4ac
Δ = -22-4·1·(-157)
Δ = 632
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:

$\sqrt{\Delta}=\sqrt{632}=\sqrt{4*158}=\sqrt{4}*\sqrt{158}=2\sqrt{158}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{158}}{2*1}=\frac{2-2\sqrt{158}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{158}}{2*1}=\frac{2+2\sqrt{158}}{2}
$