u+2/3u-1=6-u/u+1

Solution for u+2/3u-1=6-u/u+1 equation:

u+2/3u-1=6-u/u+1

We move all terms to the left:

u+2/3u-1-(6-u/u+1)=0


Domain of the equation: 3u!=0

u!=0/3

u!=0

u∈R



Domain of the equation: u+1)!=0

u∈R


We add all the numbers together, and all the variables

u+2/3u-(-u/u+7)-1=0

We get rid of parentheses

u+2/3u+u/u-7-1=0

Fractions to decimals

2/3u+u-7-1+1=0

We multiply all the terms by the denominator


u*3u-7*3u-1*3u+1*3u+2=0

Wy multiply elements

3u^2-21u-3u+3u+2=0

We add all the numbers together, and all the variables

3u^2-21u+2=0

a = 3; b = -21; c = +2;
Δ = b2-4ac
Δ = -212-4·3·2
Δ = 417
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{417}}{2*3}=\frac{21-\sqrt{417}}{6}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{417}}{2*3}=\frac{21+\sqrt{417}}{6}
$