2x/x-3=x/4

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

2x/x-3=x/4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-1x^2)/4x+8x/4x-3=0

We multiply all the terms by the denominator


(-1x^2)+8x-3*4x=0

Wy multiply elements

(-1x^2)+8x-12x=0

We get rid of parentheses

-1x^2+8x-12x=0

We add all the numbers together, and all the variables

-1x^2-4x=0

a = -1; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-1)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-1}=\frac{8}{-2}
=-4
$