1/2k+1/4k=11

Solution for 1/2k+1/4k=11 equation:

1/2k+1/4k=11

We move all terms to the left:

1/2k+1/4k-(11)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 4k!=0

k!=0/4

k!=0

k∈R


We calculate fractions


4k/8k^2+2k/8k^2-11=0

We multiply all the terms by the denominator


4k+2k-11*8k^2=0

We add all the numbers together, and all the variables

6k-11*8k^2=0

Wy multiply elements

-88k^2+6k=0

a = -88; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-88)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-88}=\frac{-12}{-176}
=3/44
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-88}=\frac{0}{-176}
=0
$