7/3x=5/x+6

Solution for 7/3x=5/x+6 equation:

7/3x=5/x+6

We move all terms to the left:

7/3x-(5/x+6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x+6)!=0

x∈R


We get rid of parentheses

7/3x-5/x-6=0

We calculate fractions


7x/3x^2+(-15x)/3x^2-6=0

We multiply all the terms by the denominator


7x+(-15x)-6*3x^2=0

Wy multiply elements

-18x^2+7x+(-15x)=0

We get rid of parentheses

-18x^2+7x-15x=0

We add all the numbers together, and all the variables

-18x^2-8x=0

a = -18; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-18)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-18}=\frac{0}{-36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-18}=\frac{16}{-36}
=-4/9
$