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

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

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

We move all terms to the left:

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

We get rid of parentheses

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


We calculate terms in parentheses: -(3x(x+2)-4), so:

3x(x+2)-4

We multiply parentheses

3x^2+6x-4

Back to the equation:

-(3x^2+6x-4)


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -3; b = -3; c = +6;
Δ = b2-4ac
Δ = -32-4·(-3)·6
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9}{2*-3}=\frac{-6}{-6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*-3}=\frac{12}{-6}
=-2
$