-8/5k+3/5=8+4/9k

Solution for -8/5k+3/5=8+4/9k equation:

-8/5k+3/5=8+4/9k

We move all terms to the left:

-8/5k+3/5-(8+4/9k)=0


Domain of the equation: 5k!=0

k!=0/5

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

-8/5k-(4/9k+8)+3/5=0

We get rid of parentheses

-8/5k-4/9k-8+3/5=0

We calculate fractions


(-72k)/1125k^2+(-500k)/1125k^2+27k/1125k^2-8=0

We multiply all the terms by the denominator


(-72k)+(-500k)+27k-8*1125k^2=0

We add all the numbers together, and all the variables

27k+(-72k)+(-500k)-8*1125k^2=0

Wy multiply elements

-9000k^2+27k+(-72k)+(-500k)=0

We get rid of parentheses

-9000k^2+27k-72k-500k=0

We add all the numbers together, and all the variables

-9000k^2-545k=0

a = -9000; b = -545; c = 0;
Δ = b2-4ac
Δ = -5452-4·(-9000)·0
Δ = 297025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{297025}=545$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-545)-545}{2*-9000}=\frac{0}{-18000}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-545)+545}{2*-9000}=\frac{1090}{-18000}
=-109/1800
$