3/8k-1/2k=3

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

3/8k-1/2k=3

We move all terms to the left:

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


Domain of the equation: 8k!=0

k!=0/8

k!=0

k∈R



Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R


We calculate fractions


6k/16k^2+(-8k)/16k^2-3=0

We multiply all the terms by the denominator


6k+(-8k)-3*16k^2=0

Wy multiply elements

-48k^2+6k+(-8k)=0

We get rid of parentheses

-48k^2+6k-8k=0

We add all the numbers together, and all the variables

-48k^2-2k=0

a = -48; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-48)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-48}=\frac{0}{-96}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-48}=\frac{4}{-96}
=-1/24
$