.5k+2=5+5/6k

Solution for .5k+2=5+5/6k equation:

.5k+2=5+5/6k

We move all terms to the left:

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


Domain of the equation: 6k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


(.5k)*6k-5*6k+2*6k-5=0

We add all the numbers together, and all the variables

(+.5k)*6k-5*6k+2*6k-5=0

We multiply parentheses

6k^2-5*6k+2*6k-5=0

Wy multiply elements

6k^2-30k+12k-5=0

We add all the numbers together, and all the variables

6k^2-18k-5=0

a = 6; b = -18; c = -5;
Δ = b2-4ac
Δ = -182-4·6·(-5)
Δ = 444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{111}}{2*6}=\frac{18-2\sqrt{111}}{12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{111}}{2*6}=\frac{18+2\sqrt{111}}{12}
$