-2/9k+7/9=-5+5/3k

Solution for -2/9k+7/9=-5+5/3k equation:

-2/9k+7/9=-5+5/3k

We move all terms to the left:

-2/9k+7/9-(-5+5/3k)=0


Domain of the equation: 9k!=0

k!=0/9

k!=0

k∈R



Domain of the equation: 3k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-2/9k-(5/3k-5)+7/9=0

We get rid of parentheses

-2/9k-5/3k+5+7/9=0

We calculate fractions


(-6k)/2187k^2+(-3645k)/2187k^2+21k/2187k^2+5=0

We multiply all the terms by the denominator


(-6k)+(-3645k)+21k+5*2187k^2=0

We add all the numbers together, and all the variables

21k+(-6k)+(-3645k)+5*2187k^2=0

Wy multiply elements

10935k^2+21k+(-6k)+(-3645k)=0

We get rid of parentheses

10935k^2+21k-6k-3645k=0

We add all the numbers together, and all the variables

10935k^2-3630k=0

a = 10935; b = -3630; c = 0;
Δ = b2-4ac
Δ = -36302-4·10935·0
Δ = 13176900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13176900}=3630$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3630)-3630}{2*10935}=\frac{0}{21870}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3630)+3630}{2*10935}=\frac{7260}{21870}
=242/729
$