(x+1)(x)=256

Solution for (x+1)(x)=256 equation:

(x+1)(x)=256

We move all terms to the left:

(x+1)(x)-(256)=0

We multiply parentheses

x^2+x-256=0

a = 1; b = 1; c = -256;
Δ = b2-4ac
Δ = 12-4·1·(-256)
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{41}}{2*1}=\frac{-1-5\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{41}}{2*1}=\frac{-1+5\sqrt{41}}{2}
$