1/2k+2=55/6k

Solution for 1/2k+2=55/6k equation:

1/2k+2=55/6k

We move all terms to the left:

1/2k+2-(55/6k)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 6k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

1/2k-(+55/6k)+2=0

We get rid of parentheses

1/2k-55/6k+2=0

We calculate fractions


6k/12k^2+(-110k)/12k^2+2=0

We multiply all the terms by the denominator


6k+(-110k)+2*12k^2=0

Wy multiply elements

24k^2+6k+(-110k)=0

We get rid of parentheses

24k^2+6k-110k=0

We add all the numbers together, and all the variables

24k^2-104k=0

a = 24; b = -104; c = 0;
Δ = b2-4ac
Δ = -1042-4·24·0
Δ = 10816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10816}=104$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-104}{2*24}=\frac{0}{48}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+104}{2*24}=\frac{208}{48}
=4+1/3
$