2/4k-2=1/k

Solution for 2/4k-2=1/k equation:

2/4k-2=1/k

We move all terms to the left:

2/4k-2-(1/k)=0


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

2/4k-(+1/k)-2=0

We get rid of parentheses

2/4k-1/k-2=0

We calculate fractions


2k/4k^2+(-4k)/4k^2-2=0

We multiply all the terms by the denominator


2k+(-4k)-2*4k^2=0

Wy multiply elements

-8k^2+2k+(-4k)=0

We get rid of parentheses

-8k^2+2k-4k=0

We add all the numbers together, and all the variables

-8k^2-2k=0

a = -8; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-8)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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