5/9k-2/3=9-5/2k

Solution for 5/9k-2/3=9-5/2k equation:

5/9k-2/3=9-5/2k

We move all terms to the left:

5/9k-2/3-(9-5/2k)=0


Domain of the equation: 9k!=0

k!=0/9

k!=0

k∈R



Domain of the equation: 2k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

5/9k-(-5/2k+9)-2/3=0

We get rid of parentheses

5/9k+5/2k-9-2/3=0

We calculate fractions


(-72k^2)/162k^2+90k/162k^2+405k/162k^2-9=0

We multiply all the terms by the denominator


(-72k^2)+90k+405k-9*162k^2=0

We add all the numbers together, and all the variables

(-72k^2)+495k-9*162k^2=0

Wy multiply elements

(-72k^2)-1458k^2+495k=0

We get rid of parentheses

-72k^2-1458k^2+495k=0

We add all the numbers together, and all the variables

-1530k^2+495k=0

a = -1530; b = 495; c = 0;
Δ = b2-4ac
Δ = 4952-4·(-1530)·0
Δ = 245025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{245025}=495$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(495)-495}{2*-1530}=\frac{-990}{-3060}
=11/34
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(495)+495}{2*-1530}=\frac{0}{-3060}
=0
$