-9/5k+-8/9=-4-1/7k

Solution for -9/5k+-8/9=-4-1/7k equation:

-9/5k+-8/9=-4-1/7k

We move all terms to the left:

-9/5k+-8/9-(-4-1/7k)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 7k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-9/5k-(-1/7k-4)+-8/9=0

We add all the numbers together, and all the variables

-9/5k-(-1/7k-4)-8/9=0

We get rid of parentheses

-9/5k+1/7k+4-8/9=0

We calculate fractions


(-1960k^2)/2835k^2+(-5103k)/2835k^2+405k/2835k^2+4=0

We multiply all the terms by the denominator


(-1960k^2)+(-5103k)+405k+4*2835k^2=0

We add all the numbers together, and all the variables

(-1960k^2)+405k+(-5103k)+4*2835k^2=0

Wy multiply elements

(-1960k^2)+11340k^2+405k+(-5103k)=0

We get rid of parentheses

-1960k^2+11340k^2+405k-5103k=0

We add all the numbers together, and all the variables

9380k^2-4698k=0

a = 9380; b = -4698; c = 0;
Δ = b2-4ac
Δ = -46982-4·9380·0
Δ = 22071204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22071204}=4698$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4698)-4698}{2*9380}=\frac{0}{18760}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4698)+4698}{2*9380}=\frac{9396}{18760}
=2349/4690
$