9/5k+6/7=-8-7/9k

Solution for 9/5k+6/7=-8-7/9k equation:

9/5k+6/7=-8-7/9k

We move all terms to the left:

9/5k+6/7-(-8-7/9k)=0


Domain of the equation: 5k!=0

k!=0/5

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

9/5k-(-7/9k-8)+6/7=0

We get rid of parentheses

9/5k+7/9k+8+6/7=0

We calculate fractions


2430k^2/2205k^2+3969k/2205k^2+1715k/2205k^2+8=0

We multiply all the terms by the denominator


2430k^2+3969k+1715k+8*2205k^2=0

We add all the numbers together, and all the variables

2430k^2+5684k+8*2205k^2=0

Wy multiply elements

2430k^2+17640k^2+5684k=0

We add all the numbers together, and all the variables

20070k^2+5684k=0

a = 20070; b = 5684; c = 0;
Δ = b2-4ac
Δ = 56842-4·20070·0
Δ = 32307856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32307856}=5684$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5684)-5684}{2*20070}=\frac{-11368}{40140}
=-2842/10035
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5684)+5684}{2*20070}=\frac{0}{40140}
=0
$