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

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

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

We move all terms to the left:

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


Domain of the equation: 6k!=0

k!=0/6

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

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

We get rid of parentheses

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

We calculate fractions


2058k^2/3402k^2+(-2835k)/3402k^2+4374k/3402k^2-2=0

We multiply all the terms by the denominator


2058k^2+(-2835k)+4374k-2*3402k^2=0

We add all the numbers together, and all the variables

2058k^2+4374k+(-2835k)-2*3402k^2=0

Wy multiply elements

2058k^2-6804k^2+4374k+(-2835k)=0

We get rid of parentheses

2058k^2-6804k^2+4374k-2835k=0

We add all the numbers together, and all the variables

-4746k^2+1539k=0

a = -4746; b = 1539; c = 0;
Δ = b2-4ac
Δ = 15392-4·(-4746)·0
Δ = 2368521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2368521}=1539$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1539)-1539}{2*-4746}=\frac{-3078}{-9492}
=513/1582
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1539)+1539}{2*-4746}=\frac{0}{-9492}
=0
$