1/7k+4/3=-9-6/5k

Solution for 1/7k+4/3=-9-6/5k equation:

1/7k+4/3=-9-6/5k

We move all terms to the left:

1/7k+4/3-(-9-6/5k)=0


Domain of the equation: 7k!=0

k!=0/7

k!=0

k∈R



Domain of the equation: 5k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

1/7k-(-6/5k-9)+4/3=0

We get rid of parentheses

1/7k+6/5k+9+4/3=0

We calculate fractions


700k^2/315k^2+45k/315k^2+378k/315k^2+9=0

We multiply all the terms by the denominator


700k^2+45k+378k+9*315k^2=0

We add all the numbers together, and all the variables

700k^2+423k+9*315k^2=0

Wy multiply elements

700k^2+2835k^2+423k=0

We add all the numbers together, and all the variables

3535k^2+423k=0

a = 3535; b = 423; c = 0;
Δ = b2-4ac
Δ = 4232-4·3535·0
Δ = 178929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{178929}=423$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(423)-423}{2*3535}=\frac{-846}{7070}
=-423/3535
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(423)+423}{2*3535}=\frac{0}{7070}
=0
$