1/2k-3=22/4k

Solution for 1/2k-3=22/4k equation:

1/2k-3=22/4k

We move all terms to the left:

1/2k-3-(22/4k)=0


Domain of the equation: 2k!=0

k!=0/2

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

1/2k-(+22/4k)-3=0

We get rid of parentheses

1/2k-22/4k-3=0

We calculate fractions


4k/8k^2+(-44k)/8k^2-3=0

We multiply all the terms by the denominator


4k+(-44k)-3*8k^2=0

Wy multiply elements

-24k^2+4k+(-44k)=0

We get rid of parentheses

-24k^2+4k-44k=0

We add all the numbers together, and all the variables

-24k^2-40k=0

a = -24; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·(-24)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*-24}=\frac{0}{-48}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*-24}=\frac{80}{-48}
=-1+2/3
$