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

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

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

We move all terms to the left:

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


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 5k+k)!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


-k+()/10k+5k/10k-1=0

We add all the numbers together, and all the variables

-1k+()/10k+5k/10k-1=0

We multiply all the terms by the denominator


-1k*10k+5k-1*10k+()=0

We add all the numbers together, and all the variables

5k-1k*10k-1*10k=0

Wy multiply elements

-10k^2+5k-10k=0

We add all the numbers together, and all the variables

-10k^2-5k=0

a = -10; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-10)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-10}=\frac{0}{-20}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-10}=\frac{10}{-20}
=-1/2
$