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

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

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

We move all terms to the left:

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


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 4k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


4k/12k^2+9k/12k^2-2-3=0

We add all the numbers together, and all the variables

4k/12k^2+9k/12k^2-5=0

We multiply all the terms by the denominator


4k+9k-5*12k^2=0

We add all the numbers together, and all the variables

13k-5*12k^2=0

Wy multiply elements

-60k^2+13k=0

a = -60; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-60)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-60}=\frac{-26}{-120}
=13/60
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-60}=\frac{0}{-120}
=0
$