5/6u+2-u=1/6u

Solution for 5/6u+2-u=1/6u equation:

5/6u+2-u=1/6u

We move all terms to the left:

5/6u+2-u-(1/6u)=0


Domain of the equation: 6u!=0

u!=0/6

u!=0

u∈R



Domain of the equation: 6u)!=0

u!=0/1

u!=0

u∈R


We add all the numbers together, and all the variables

5/6u-u-(+1/6u)+2=0

We add all the numbers together, and all the variables

-1u+5/6u-(+1/6u)+2=0

We get rid of parentheses

-1u+5/6u-1/6u+2=0

We multiply all the terms by the denominator


-1u*6u+2*6u+5-1=0

We add all the numbers together, and all the variables

-1u*6u+2*6u+4=0

Wy multiply elements

-6u^2+12u+4=0

a = -6; b = 12; c = +4;
Δ = b2-4ac
Δ = 122-4·(-6)·4
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{15}}{2*-6}=\frac{-12-4\sqrt{15}}{-12}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{15}}{2*-6}=\frac{-12+4\sqrt{15}}{-12}
$