1/2k=4/3k+1

Solution for 1/2k=4/3k+1 equation:

1/2k=4/3k+1

We move all terms to the left:

1/2k-(4/3k+1)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 3k+1)!=0

k∈R


We get rid of parentheses

1/2k-4/3k-1=0

We calculate fractions


3k/6k^2+(-8k)/6k^2-1=0

We multiply all the terms by the denominator


3k+(-8k)-1*6k^2=0

Wy multiply elements

-6k^2+3k+(-8k)=0

We get rid of parentheses

-6k^2+3k-8k=0

We add all the numbers together, and all the variables

-6k^2-5k=0

a = -6; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-6)·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*-6}=\frac{0}{-12}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-6}=\frac{10}{-12}
=-5/6
$