9/5k-3/5=-8+2/9k

Solution for 9/5k-3/5=-8+2/9k equation:

9/5k-3/5=-8+2/9k

We move all terms to the left:

9/5k-3/5-(-8+2/9k)=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-(2/9k-8)-3/5=0

We get rid of parentheses

9/5k-2/9k+8-3/5=0

We calculate fractions


81k/1125k^2+(-250k)/1125k^2+(-27k)/1125k^2+8=0

We multiply all the terms by the denominator


81k+(-250k)+(-27k)+8*1125k^2=0

Wy multiply elements

9000k^2+81k+(-250k)+(-27k)=0

We get rid of parentheses

9000k^2+81k-250k-27k=0

We add all the numbers together, and all the variables

9000k^2-196k=0

a = 9000; b = -196; c = 0;
Δ = b2-4ac
Δ = -1962-4·9000·0
Δ = 38416
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{38416}=196$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-196)-196}{2*9000}=\frac{0}{18000}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-196)+196}{2*9000}=\frac{392}{18000}
=49/2250
$