1/2k=3/4k+1

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

1/2k=3/4k+1

We move all terms to the left:

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


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 4k+1)!=0

k∈R


We get rid of parentheses

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

We calculate fractions


4k/8k^2+(-6k)/8k^2-1=0

We multiply all the terms by the denominator


4k+(-6k)-1*8k^2=0

Wy multiply elements

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

We get rid of parentheses

-8k^2+4k-6k=0

We add all the numbers together, and all the variables

-8k^2-2k=0

a = -8; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-8)·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*-8}=\frac{0}{-16}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-8}=\frac{4}{-16}
=-1/4
$