5/6k+5/8=6-5/9k

Solution for 5/6k+5/8=6-5/9k equation:

5/6k+5/8=6-5/9k

We move all terms to the left:

5/6k+5/8-(6-5/9k)=0


Domain of the equation: 6k!=0

k!=0/6

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

5/6k-(-5/9k+6)+5/8=0

We get rid of parentheses

5/6k+5/9k-6+5/8=0

We calculate fractions


2430k^2/3456k^2+2880k/3456k^2+1920k/3456k^2-6=0

We multiply all the terms by the denominator


2430k^2+2880k+1920k-6*3456k^2=0

We add all the numbers together, and all the variables

2430k^2+4800k-6*3456k^2=0

Wy multiply elements

2430k^2-20736k^2+4800k=0

We add all the numbers together, and all the variables

-18306k^2+4800k=0

a = -18306; b = 4800; c = 0;
Δ = b2-4ac
Δ = 48002-4·(-18306)·0
Δ = 23040000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{23040000}=4800$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4800)-4800}{2*-18306}=\frac{-9600}{-36612}
=800/3051
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4800)+4800}{2*-18306}=\frac{0}{-36612}
=0
$