5/4x-1=9/3x-4

Solution for 5/4x-1=9/3x-4 equation:

5/4x-1=9/3x-4

We move all terms to the left:

5/4x-1-(9/3x-4)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

5/4x-9/3x+4-1=0

We calculate fractions


15x/12x^2+(-36x)/12x^2+4-1=0

We add all the numbers together, and all the variables

15x/12x^2+(-36x)/12x^2+3=0

We multiply all the terms by the denominator


15x+(-36x)+3*12x^2=0

Wy multiply elements

36x^2+15x+(-36x)=0

We get rid of parentheses

36x^2+15x-36x=0

We add all the numbers together, and all the variables

36x^2-21x=0

a = 36; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·36·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*36}=\frac{0}{72}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*36}=\frac{42}{72}
=7/12
$