-1/7k+8/5=-2-5/9k

Solution for -1/7k+8/5=-2-5/9k equation:

-1/7k+8/5=-2-5/9k

We move all terms to the left:

-1/7k+8/5-(-2-5/9k)=0


Domain of the equation: 7k!=0

k!=0/7

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

-1/7k-(-5/9k-2)+8/5=0

We get rid of parentheses

-1/7k+5/9k+2+8/5=0

We calculate fractions


4536k^2/1575k^2+(-225k)/1575k^2+875k/1575k^2+2=0

We multiply all the terms by the denominator


4536k^2+(-225k)+875k+2*1575k^2=0

We add all the numbers together, and all the variables

4536k^2+875k+(-225k)+2*1575k^2=0

Wy multiply elements

4536k^2+3150k^2+875k+(-225k)=0

We get rid of parentheses

4536k^2+3150k^2+875k-225k=0

We add all the numbers together, and all the variables

7686k^2+650k=0

a = 7686; b = 650; c = 0;
Δ = b2-4ac
Δ = 6502-4·7686·0
Δ = 422500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{422500}=650$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(650)-650}{2*7686}=\frac{-1300}{15372}
=-325/3843
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(650)+650}{2*7686}=\frac{0}{15372}
=0
$