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