1/2k-1/4=5/8k+2

Solution for 1/2k-1/4=5/8k+2 equation:

1/2k-1/4=5/8k+2

We move all terms to the left:

1/2k-1/4-(5/8k+2)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 8k+2)!=0

k∈R


We get rid of parentheses

1/2k-5/8k-2-1/4=0

We calculate fractions


(-128k^2)/256k^2+128k/256k^2+(-160k)/256k^2-2=0

We multiply all the terms by the denominator


(-128k^2)+128k+(-160k)-2*256k^2=0

Wy multiply elements

(-128k^2)-512k^2+128k+(-160k)=0

We get rid of parentheses

-128k^2-512k^2+128k-160k=0

We add all the numbers together, and all the variables

-640k^2-32k=0

a = -640; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-640)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-640}=\frac{0}{-1280}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-640}=\frac{64}{-1280}
=-1/20
$