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

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

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

We move all terms to the left:

2-3/2k-(1/8k+9)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 8k+9)!=0

k∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

(-24k)/16k^2+(-2k)/16k^2-7=0

We multiply all the terms by the denominator


(-24k)+(-2k)-7*16k^2=0

Wy multiply elements

-112k^2+(-24k)+(-2k)=0

We get rid of parentheses

-112k^2-24k-2k=0

We add all the numbers together, and all the variables

-112k^2-26k=0

a = -112; b = -26; c = 0;
Δ = b2-4ac
Δ = -262-4·(-112)·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-26}{2*-112}=\frac{0}{-224}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+26}{2*-112}=\frac{52}{-224}
=-13/56
$