(6x-4)=4(3/2x-1)

Solution for (6x-4)=4(3/2x-1) equation:

(6x-4)=4(3/2x-1)

We move all terms to the left:

(6x-4)-(4(3/2x-1))=0


Domain of the equation: 2x-1))!=0

x∈R


We get rid of parentheses

6x-(4(3/2x-1))-4=0

We multiply all the terms by the denominator


6x*2x-4*2x-1))-(4(3-1))=0

We add all the numbers together, and all the variables

6x*2x-4*2x-1))-(42)=0

We add all the numbers together, and all the variables

6x*2x-4*2x=0

Wy multiply elements

12x^2-8x=0

a = 12; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·12·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*12}=\frac{16}{24}
=2/3
$