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

Solution for x(2x-1)+(2x-1)=0 equation:

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

We multiply parentheses

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

We get rid of parentheses

2x^2-1x+2x-1=0

We add all the numbers together, and all the variables

2x^2+x-1=0

a = 2; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·2·(-1)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3}{2*2}=\frac{-4}{4}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3}{2*2}=\frac{2}{4}
=1/2
$