1/2*k+2=5+5/6k

Solution for 1/2*k+2=5+5/6k equation:

1/2k+2=5+5/6k

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


6k/12k^2+(-10k)/12k^2-5+2=0

We add all the numbers together, and all the variables

6k/12k^2+(-10k)/12k^2-3=0

We multiply all the terms by the denominator


6k+(-10k)-3*12k^2=0

Wy multiply elements

-36k^2+6k+(-10k)=0

We get rid of parentheses

-36k^2+6k-10k=0

We add all the numbers together, and all the variables

-36k^2-4k=0

a = -36; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-36)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-36}=\frac{0}{-72}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-36}=\frac{8}{-72}
=-1/9
$