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

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

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

We move all terms to the left:

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


Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R



Domain of the equation: 8k!=0

k!=0/8

k!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-256k^2)/288k^2+216k/288k^2+(-108k)/288k^2=0

We multiply all the terms by the denominator


(-256k^2)+216k+(-108k)=0

We get rid of parentheses

-256k^2+216k-108k=0

We add all the numbers together, and all the variables

-256k^2+108k=0

a = -256; b = 108; c = 0;
Δ = b2-4ac
Δ = 1082-4·(-256)·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108}{2*-256}=\frac{-216}{-512}
=27/64
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108}{2*-256}=\frac{0}{-512}
=0
$