(4x-1)(2x+3)=2x

Solution for (4x-1)(2x+3)=2x equation:

(4x-1)(2x+3)=2x

We move all terms to the left:

(4x-1)(2x+3)-(2x)=0

We add all the numbers together, and all the variables

-2x+(4x-1)(2x+3)=0

We multiply parentheses ..

(+8x^2+12x-2x-3)-2x=0

We get rid of parentheses

8x^2+12x-2x-2x-3=0

We add all the numbers together, and all the variables

8x^2+8x-3=0

a = 8; b = 8; c = -3;
Δ = b2-4ac
Δ = 82-4·8·(-3)
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{10}}{2*8}=\frac{-8-4\sqrt{10}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{10}}{2*8}=\frac{-8+4\sqrt{10}}{16}
$