3/x-5/4x=5/3

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

3/x-5/4x=5/3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/x-5/4x-(+5/3)=0

We get rid of parentheses

3/x-5/4x-5/3=0

We calculate fractions


(-80x^2)/36x^2+108x/36x^2+(-45x)/36x^2=0

We multiply all the terms by the denominator


(-80x^2)+108x+(-45x)=0

We get rid of parentheses

-80x^2+108x-45x=0

We add all the numbers together, and all the variables

-80x^2+63x=0

a = -80; b = 63; c = 0;
Δ = b2-4ac
Δ = 632-4·(-80)·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-63}{2*-80}=\frac{-126}{-160}
=63/80
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*-80}=\frac{0}{-160}
=0
$