1/x=3-5/3x

Solution for 1/x=3-5/3x equation:

1/x=3-5/3x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/x+5/3x-3=0

We calculate fractions


3x/3x^2+5x/3x^2-3=0

We multiply all the terms by the denominator


3x+5x-3*3x^2=0

We add all the numbers together, and all the variables

8x-3*3x^2=0

Wy multiply elements

-9x^2+8x=0

a = -9; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-9)·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*-9}=\frac{-16}{-18}
=8/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-9}=\frac{0}{-18}
=0
$