9/5k-8/3=2-3/7k

Solution for 9/5k-8/3=2-3/7k equation:

9/5k-8/3=2-3/7k

We move all terms to the left:

9/5k-8/3-(2-3/7k)=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-(-3/7k+2)-8/3=0

We get rid of parentheses

9/5k+3/7k-2-8/3=0

We calculate fractions


(-1960k^2)/315k^2+567k/315k^2+135k/315k^2-2=0

We multiply all the terms by the denominator


(-1960k^2)+567k+135k-2*315k^2=0

We add all the numbers together, and all the variables

(-1960k^2)+702k-2*315k^2=0

Wy multiply elements

(-1960k^2)-630k^2+702k=0

We get rid of parentheses

-1960k^2-630k^2+702k=0

We add all the numbers together, and all the variables

-2590k^2+702k=0

a = -2590; b = 702; c = 0;
Δ = b2-4ac
Δ = 7022-4·(-2590)·0
Δ = 492804
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{492804}=702$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(702)-702}{2*-2590}=\frac{-1404}{-5180}
=351/1295
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(702)+702}{2*-2590}=\frac{0}{-5180}
=0
$