x(2x-1)=91

Solution for x(2x-1)=91 equation:

x(2x-1)=91

We move all terms to the left:

x(2x-1)-(91)=0

We multiply parentheses

2x^2-1x-91=0

a = 2; b = -1; c = -91;
Δ = b2-4ac
Δ = -12-4·2·(-91)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-27}{2*2}=\frac{-26}{4}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+27}{2*2}=\frac{28}{4}
=7
$