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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(3(2x-1)), so:

3(2x-1)

We multiply parentheses

6x-3

Back to the equation:

-(6x-3)


We add all the numbers together, and all the variables

-4x^2-2x-(6x-3)=0

We get rid of parentheses

-4x^2-2x-6x+3=0

We add all the numbers together, and all the variables

-4x^2-8x+3=0

a = -4; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·(-4)·3
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{7}}{2*-4}=\frac{8-4\sqrt{7}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{7}}{2*-4}=\frac{8+4\sqrt{7}}{-8}
$