3/2k-9=1/8k+2

Solution for 3/2k-9=1/8k+2 equation:

3/2k-9=1/8k+2

We move all terms to the left:

3/2k-9-(1/8k+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

3/2k-1/8k-2-9=0

We calculate fractions


24k/16k^2+(-2k)/16k^2-2-9=0

We add all the numbers together, and all the variables

24k/16k^2+(-2k)/16k^2-11=0

We multiply all the terms by the denominator


24k+(-2k)-11*16k^2=0

Wy multiply elements

-176k^2+24k+(-2k)=0

We get rid of parentheses

-176k^2+24k-2k=0

We add all the numbers together, and all the variables

-176k^2+22k=0

a = -176; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-176)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-176}=\frac{-44}{-352}
=1/8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-176}=\frac{0}{-352}
=0
$