(x-1)(x)=91

Solution for (x-1)(x)=91 equation:

(x-1)(x)=91

We move all terms to the left:

(x-1)(x)-(91)=0

We multiply parentheses

x^2-1x-91=0

a = 1; b = -1; c = -91;
Δ = b2-4ac
Δ = -12-4·1·(-91)
Δ = 365
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{365}}{2*1}=\frac{1-\sqrt{365}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{365}}{2*1}=\frac{1+\sqrt{365}}{2}
$