5+31/2k=21/4k+6

Solution for 5+31/2k=21/4k+6 equation:

5+31/2k=21/4k+6

We move all terms to the left:

5+31/2k-(21/4k+6)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 4k+6)!=0

k∈R


We get rid of parentheses

31/2k-21/4k-6+5=0

We calculate fractions


124k/8k^2+(-42k)/8k^2-6+5=0

We add all the numbers together, and all the variables

124k/8k^2+(-42k)/8k^2-1=0

We multiply all the terms by the denominator


124k+(-42k)-1*8k^2=0

Wy multiply elements

-8k^2+124k+(-42k)=0

We get rid of parentheses

-8k^2+124k-42k=0

We add all the numbers together, and all the variables

-8k^2+82k=0

a = -8; b = 82; c = 0;
Δ = b2-4ac
Δ = 822-4·(-8)·0
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-82}{2*-8}=\frac{-164}{-16}
=10+1/4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+82}{2*-8}=\frac{0}{-16}
=0
$