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

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

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

We move all terms to the left:

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


Domain of the equation: 7k!=0

k!=0/7

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

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

We get rid of parentheses

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

We calculate fractions


(-3402k^2)/1575k^2+900k/1575k^2+1400k/1575k^2-2=0

We multiply all the terms by the denominator


(-3402k^2)+900k+1400k-2*1575k^2=0

We add all the numbers together, and all the variables

(-3402k^2)+2300k-2*1575k^2=0

Wy multiply elements

(-3402k^2)-3150k^2+2300k=0

We get rid of parentheses

-3402k^2-3150k^2+2300k=0

We add all the numbers together, and all the variables

-6552k^2+2300k=0

a = -6552; b = 2300; c = 0;
Δ = b2-4ac
Δ = 23002-4·(-6552)·0
Δ = 5290000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5290000}=2300$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2300)-2300}{2*-6552}=\frac{-4600}{-13104}
=575/1638
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2300)+2300}{2*-6552}=\frac{0}{-13104}
=0
$