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

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

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

We move all terms to the left:

1/3k-8-(4-3/4k)=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+4)-8=0

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

13k-12*12k^2=0

Wy multiply elements

-144k^2+13k=0

a = -144; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-144)·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*-144}=\frac{-26}{-288}
=13/144
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-144}=\frac{0}{-288}
=0
$