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

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

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

We move all terms to the left:

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


Domain of the equation: 9k!=0

k!=0/9

k!=0

k∈R



Domain of the equation: 5k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


25k/3645k^2+(-2187k)/3645k^2+(-10k)/3645k^2+3=0

We multiply all the terms by the denominator


25k+(-2187k)+(-10k)+3*3645k^2=0

Wy multiply elements

10935k^2+25k+(-2187k)+(-10k)=0

We get rid of parentheses

10935k^2+25k-2187k-10k=0

We add all the numbers together, and all the variables

10935k^2-2172k=0

a = 10935; b = -2172; c = 0;
Δ = b2-4ac
Δ = -21722-4·10935·0
Δ = 4717584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4717584}=2172$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2172)-2172}{2*10935}=\frac{0}{21870}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2172)+2172}{2*10935}=\frac{4344}{21870}
=724/3645
$