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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-18x^2)/75x^2+300x/75x^2+(-175x)/75x^2=0

We multiply all the terms by the denominator


(-18x^2)+300x+(-175x)=0

We get rid of parentheses

-18x^2+300x-175x=0

We add all the numbers together, and all the variables

-18x^2+125x=0

a = -18; b = 125; c = 0;
Δ = b2-4ac
Δ = 1252-4·(-18)·0
Δ = 15625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15625}=125$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-125}{2*-18}=\frac{-250}{-36}
=6+17/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+125}{2*-18}=\frac{0}{-36}
=0
$