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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


4k/8k^2+(-6k)/8k^2-2-3=0

We add all the numbers together, and all the variables

4k/8k^2+(-6k)/8k^2-5=0

We multiply all the terms by the denominator


4k+(-6k)-5*8k^2=0

Wy multiply elements

-40k^2+4k+(-6k)=0

We get rid of parentheses

-40k^2+4k-6k=0

We add all the numbers together, and all the variables

-40k^2-2k=0

a = -40; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-40)·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*-40}=\frac{0}{-80}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-40}=\frac{4}{-80}
=-1/20
$