-5/6k+8/7=7-8/9k

Solution for -5/6k+8/7=7-8/9k equation:

-5/6k+8/7=7-8/9k

We move all terms to the left:

-5/6k+8/7-(7-8/9k)=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-(-8/9k+7)+8/7=0

We get rid of parentheses

-5/6k+8/9k-7+8/7=0

We calculate fractions


3888k^2/2646k^2+(-2205k)/2646k^2+2352k/2646k^2-7=0

We multiply all the terms by the denominator


3888k^2+(-2205k)+2352k-7*2646k^2=0

We add all the numbers together, and all the variables

3888k^2+2352k+(-2205k)-7*2646k^2=0

Wy multiply elements

3888k^2-18522k^2+2352k+(-2205k)=0

We get rid of parentheses

3888k^2-18522k^2+2352k-2205k=0

We add all the numbers together, and all the variables

-14634k^2+147k=0

a = -14634; b = 147; c = 0;
Δ = b2-4ac
Δ = 1472-4·(-14634)·0
Δ = 21609
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21609}=147$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(147)-147}{2*-14634}=\frac{-294}{-29268}
=49/4878
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(147)+147}{2*-14634}=\frac{0}{-29268}
=0
$