6/7k+2/9=-3-9/5k

Solution for 6/7k+2/9=-3-9/5k equation:

6/7k+2/9=-3-9/5k

We move all terms to the left:

6/7k+2/9-(-3-9/5k)=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

6/7k-(-9/5k-3)+2/9=0

We get rid of parentheses

6/7k+9/5k+3+2/9=0

We calculate fractions


350k^2/2835k^2+2430k/2835k^2+5103k/2835k^2+3=0

We multiply all the terms by the denominator


350k^2+2430k+5103k+3*2835k^2=0

We add all the numbers together, and all the variables

350k^2+7533k+3*2835k^2=0

Wy multiply elements

350k^2+8505k^2+7533k=0

We add all the numbers together, and all the variables

8855k^2+7533k=0

a = 8855; b = 7533; c = 0;
Δ = b2-4ac
Δ = 75332-4·8855·0
Δ = 56746089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{56746089}=7533$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7533)-7533}{2*8855}=\frac{-15066}{17710}
=-7533/8855
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7533)+7533}{2*8855}=\frac{0}{17710}
=0
$