3/3k-5=1/4k-1

Solution for 3/3k-5=1/4k-1 equation:

3/3k-5=1/4k-1

We move all terms to the left:

3/3k-5-(1/4k-1)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 4k-1)!=0

k∈R


We get rid of parentheses

3/3k-1/4k+1-5=0

We calculate fractions


12k/12k^2+(-3k)/12k^2+1-5=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-48k^2+12k+(-3k)=0

We get rid of parentheses

-48k^2+12k-3k=0

We add all the numbers together, and all the variables

-48k^2+9k=0

a = -48; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-48)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-48}=\frac{-18}{-96}
=3/16
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-48}=\frac{0}{-96}
=0
$