2/x-3=3/4x-1

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

2/x-3=3/4x-1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x-1)!=0

x∈R


We get rid of parentheses

2/x-3/4x+1-3=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-8x^2+5x=0

a = -8; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-8)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-8}=\frac{-10}{-16}
=5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-8}=\frac{0}{-16}
=0
$