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

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

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

We move all terms to the left:

-2/5k-5/9-(-9/7k)=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 get rid of parentheses

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

We calculate fractions


(-1225k^2)/2835k^2+(-1134k)/2835k^2+3645k/2835k^2=0

We multiply all the terms by the denominator


(-1225k^2)+(-1134k)+3645k=0

We add all the numbers together, and all the variables

(-1225k^2)+3645k+(-1134k)=0

We get rid of parentheses

-1225k^2+3645k-1134k=0

We add all the numbers together, and all the variables

-1225k^2+2511k=0

a = -1225; b = 2511; c = 0;
Δ = b2-4ac
Δ = 25112-4·(-1225)·0
Δ = 6305121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6305121}=2511$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2511)-2511}{2*-1225}=\frac{-5022}{-2450}
=2+61/1225
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2511)+2511}{2*-1225}=\frac{0}{-2450}
=0
$