5x-3/3=6/x

Solution for 5x-3/3=6/x equation:

5x-3/3=6/x

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

5x-(+6/x)-1=0

We get rid of parentheses

5x-6/x-1=0

We multiply all the terms by the denominator


5x*x-1*x-6=0

We add all the numbers together, and all the variables

-1x+5x*x-6=0

Wy multiply elements

5x^2-1x-6=0

a = 5; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·5·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*5}=\frac{12}{10}
=1+1/5
$