3(3u-1)=2/u

Solution for 3(3u-1)=2/u equation:

3(3u-1)=2/u

We move all terms to the left:

3(3u-1)-(2/u)=0


Domain of the equation: u)!=0

u!=0/1

u!=0

u∈R


We add all the numbers together, and all the variables

3(3u-1)-(+2/u)=0

We multiply parentheses

9u-(+2/u)-3=0

We get rid of parentheses

9u-2/u-3=0

We multiply all the terms by the denominator


9u*u-3*u-2=0

We add all the numbers together, and all the variables

-3u+9u*u-2=0

Wy multiply elements

9u^2-3u-2=0

a = 9; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·9·(-2)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9}{2*9}=\frac{-6}{18}
=-1/3
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*9}=\frac{12}{18}
=2/3
$