-8/3k+1/2=-8-3/2k

Solution for -8/3k+1/2=-8-3/2k equation:

-8/3k+1/2=-8-3/2k

We move all terms to the left:

-8/3k+1/2-(-8-3/2k)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 2k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-8/3k-(-3/2k-8)+1/2=0

We get rid of parentheses

-8/3k+3/2k+8+1/2=0

We calculate fractions


(-64k)/24k^2+9k/24k^2+3k/24k^2+8=0

We multiply all the terms by the denominator


(-64k)+9k+3k+8*24k^2=0

We add all the numbers together, and all the variables

12k+(-64k)+8*24k^2=0

Wy multiply elements

192k^2+12k+(-64k)=0

We get rid of parentheses

192k^2+12k-64k=0

We add all the numbers together, and all the variables

192k^2-52k=0

a = 192; b = -52; c = 0;
Δ = b2-4ac
Δ = -522-4·192·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-52}{2*192}=\frac{0}{384}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+52}{2*192}=\frac{104}{384}
=13/48
$