3k-2=1/2k+1

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

3k-2=1/2k+1

We move all terms to the left:

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


Domain of the equation: 2k+1)!=0

k∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


3k*2k-1*2k-2*2k-1=0

Wy multiply elements

6k^2-2k-4k-1=0

We add all the numbers together, and all the variables

6k^2-6k-1=0

a = 6; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·6·(-1)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{15}}{2*6}=\frac{6-2\sqrt{15}}{12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{15}}{2*6}=\frac{6+2\sqrt{15}}{12}
$