3/4k-3/8k=1/2

Solution for 3/4k-3/8k=1/2 equation:

3/4k-3/8k=1/2

We move all terms to the left:

3/4k-3/8k-(1/2)=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-(+1/2)=0

We get rid of parentheses

3/4k-3/8k-1/2=0

We calculate fractions


(-256k^2)/128k^2+96k/128k^2+(-48k)/128k^2=0

We multiply all the terms by the denominator


(-256k^2)+96k+(-48k)=0

We get rid of parentheses

-256k^2+96k-48k=0

We add all the numbers together, and all the variables

-256k^2+48k=0

a = -256; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·(-256)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*-256}=\frac{-96}{-512}
=3/16
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*-256}=\frac{0}{-512}
=0
$