1/3k-8=3/4k

Solution for 1/3k-8=3/4k equation:

1/3k-8=3/4k

We move all terms to the left:

1/3k-8-(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)-8=0

We get rid of parentheses

1/3k-3/4k-8=0

We calculate fractions


4k/12k^2+(-9k)/12k^2-8=0

We multiply all the terms by the denominator


4k+(-9k)-8*12k^2=0

Wy multiply elements

-96k^2+4k+(-9k)=0

We get rid of parentheses

-96k^2+4k-9k=0

We add all the numbers together, and all the variables

-96k^2-5k=0

a = -96; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-96)·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*-96}=\frac{0}{-192}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-96}=\frac{10}{-192}
=-5/96
$