3/2k+1/9=2+5/9k

Solution for 3/2k+1/9=2+5/9k equation:

3/2k+1/9=2+5/9k

We move all terms to the left:

3/2k+1/9-(2+5/9k)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 9k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

3/2k-(5/9k+2)+1/9=0

We get rid of parentheses

3/2k-5/9k-2+1/9=0

We calculate fractions


2187k/1458k^2+(-10k)/1458k^2+2k/1458k^2-2=0

We multiply all the terms by the denominator


2187k+(-10k)+2k-2*1458k^2=0

We add all the numbers together, and all the variables

2189k+(-10k)-2*1458k^2=0

Wy multiply elements

-2916k^2+2189k+(-10k)=0

We get rid of parentheses

-2916k^2+2189k-10k=0

We add all the numbers together, and all the variables

-2916k^2+2179k=0

a = -2916; b = 2179; c = 0;
Δ = b2-4ac
Δ = 21792-4·(-2916)·0
Δ = 4748041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4748041}=2179$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2179)-2179}{2*-2916}=\frac{-4358}{-5832}
=2179/2916
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2179)+2179}{2*-2916}=\frac{0}{-5832}
=0
$