8/9k+2/5=-4+2/5k

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

8/9k+2/5=-4+2/5k

We move all terms to the left:

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


Domain of the equation: 9k!=0

k!=0/9

k!=0

k∈R



Domain of the equation: 5k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


1000k/1125k^2+(-18k)/1125k^2+18k/1125k^2+4=0

We multiply all the terms by the denominator


1000k+(-18k)+18k+4*1125k^2=0

We add all the numbers together, and all the variables

1018k+(-18k)+4*1125k^2=0

Wy multiply elements

4500k^2+1018k+(-18k)=0

We get rid of parentheses

4500k^2+1018k-18k=0

We add all the numbers together, and all the variables

4500k^2+1000k=0

a = 4500; b = 1000; c = 0;
Δ = b2-4ac
Δ = 10002-4·4500·0
Δ = 1000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1000000}=1000$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1000)-1000}{2*4500}=\frac{-2000}{9000}
=-2/9
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1000)+1000}{2*4500}=\frac{0}{9000}
=0
$