2/7k-8/9=-6-5/4k

Solution for 2/7k-8/9=-6-5/4k equation:

2/7k-8/9=-6-5/4k

We move all terms to the left:

2/7k-8/9-(-6-5/4k)=0


Domain of the equation: 7k!=0

k!=0/7

k!=0

k∈R



Domain of the equation: 4k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

2/7k-(-5/4k-6)-8/9=0

We get rid of parentheses

2/7k+5/4k+6-8/9=0

We calculate fractions


(-896k^2)/2268k^2+648k/2268k^2+2835k/2268k^2+6=0

We multiply all the terms by the denominator


(-896k^2)+648k+2835k+6*2268k^2=0

We add all the numbers together, and all the variables

(-896k^2)+3483k+6*2268k^2=0

Wy multiply elements

(-896k^2)+13608k^2+3483k=0

We get rid of parentheses

-896k^2+13608k^2+3483k=0

We add all the numbers together, and all the variables

12712k^2+3483k=0

a = 12712; b = 3483; c = 0;
Δ = b2-4ac
Δ = 34832-4·12712·0
Δ = 12131289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12131289}=3483$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3483)-3483}{2*12712}=\frac{-6966}{25424}
=-3483/12712
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3483)+3483}{2*12712}=\frac{0}{25424}
=0
$