(2x-1)(x+3)=2x

Solution for (2x-1)(x+3)=2x equation:

(2x-1)(x+3)=2x

We move all terms to the left:

(2x-1)(x+3)-(2x)=0

We add all the numbers together, and all the variables

-2x+(2x-1)(x+3)=0

We multiply parentheses ..

(+2x^2+6x-1x-3)-2x=0

We get rid of parentheses

2x^2+6x-1x-2x-3=0

We add all the numbers together, and all the variables

2x^2+3x-3=0

a = 2; b = 3; c = -3;
Δ = b2-4ac
Δ = 32-4·2·(-3)
Δ = 33
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{-(3)-\sqrt{33}}{2*2}=\frac{-3-\sqrt{33}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33}}{2*2}=\frac{-3+\sqrt{33}}{4}
$