5/4x-1=7/3x-2

Solution for 5/4x-1=7/3x-2 equation:

5/4x-1=7/3x-2

We move all terms to the left:

5/4x-1-(7/3x-2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

5/4x-7/3x+2-1=0

We calculate fractions


15x/12x^2+(-28x)/12x^2+2-1=0

We add all the numbers together, and all the variables

15x/12x^2+(-28x)/12x^2+1=0

We multiply all the terms by the denominator


15x+(-28x)+1*12x^2=0

Wy multiply elements

12x^2+15x+(-28x)=0

We get rid of parentheses

12x^2+15x-28x=0

We add all the numbers together, and all the variables

12x^2-13x=0

a = 12; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·12·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*12}=\frac{26}{24}
=1+1/12
$