3/5k+-7/9=8-8/3k

Solution for 3/5k+-7/9=8-8/3k equation:

3/5k+-7/9=8-8/3k

We move all terms to the left:

3/5k+-7/9-(8-8/3k)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 3k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

3/5k-(-8/3k+8)+-7/9=0

We add all the numbers together, and all the variables

3/5k-(-8/3k+8)-7/9=0

We get rid of parentheses

3/5k+8/3k-8-7/9=0

We calculate fractions


(-315k^2)/1215k^2+729k/1215k^2+3240k/1215k^2-8=0

We multiply all the terms by the denominator


(-315k^2)+729k+3240k-8*1215k^2=0

We add all the numbers together, and all the variables

(-315k^2)+3969k-8*1215k^2=0

Wy multiply elements

(-315k^2)-9720k^2+3969k=0

We get rid of parentheses

-315k^2-9720k^2+3969k=0

We add all the numbers together, and all the variables

-10035k^2+3969k=0

a = -10035; b = 3969; c = 0;
Δ = b2-4ac
Δ = 39692-4·(-10035)·0
Δ = 15752961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15752961}=3969$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3969)-3969}{2*-10035}=\frac{-7938}{-20070}
=441/1115
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3969)+3969}{2*-10035}=\frac{0}{-20070}
=0
$