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

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

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

We move all terms to the left:

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


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 5k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

5k/10k^2+(-12k)/10k^2-3=0

We multiply all the terms by the denominator


5k+(-12k)-3*10k^2=0

Wy multiply elements

-30k^2+5k+(-12k)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-30k^2-7k=0

a = -30; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-30)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-30}=\frac{0}{-60}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-30}=\frac{14}{-60}
=-7/30
$