2/2x-3=x/4x-6

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

2/2x-3=x/4x-6

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-6)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-2x^2)/8x^2+8x/8x^2+6-3=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

(-2x^2)+24x^2+8x=0

We get rid of parentheses

-2x^2+24x^2+8x=0

We add all the numbers together, and all the variables

22x^2+8x=0

a = 22; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·22·0
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*22}=\frac{-16}{44}
=-4/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*22}=\frac{0}{44}
=0
$