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

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

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

We move all terms to the left:

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


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 4k-2)!=0

k∈R


We get rid of parentheses

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

We calculate fractions


4k/12k^2+(-3k)/12k^2+2+1=0

We add all the numbers together, and all the variables

4k/12k^2+(-3k)/12k^2+3=0

We multiply all the terms by the denominator


4k+(-3k)+3*12k^2=0

Wy multiply elements

36k^2+4k+(-3k)=0

We get rid of parentheses

36k^2+4k-3k=0

We add all the numbers together, and all the variables

36k^2+k=0

a = 36; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·36·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*36}=\frac{-2}{72}
=-1/36
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*36}=\frac{0}{72}
=0
$