7/5k-1/5=4-8/9k

Solution for 7/5k-1/5=4-8/9k equation:

7/5k-1/5=4-8/9k

We move all terms to the left:

7/5k-1/5-(4-8/9k)=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

7/5k-(-8/9k+4)-1/5=0

We get rid of parentheses

7/5k+8/9k-4-1/5=0

We calculate fractions


63k/1125k^2+1000k/1125k^2+(-9k)/1125k^2-4=0

We multiply all the terms by the denominator


63k+1000k+(-9k)-4*1125k^2=0

We add all the numbers together, and all the variables

1063k+(-9k)-4*1125k^2=0

Wy multiply elements

-4500k^2+1063k+(-9k)=0

We get rid of parentheses

-4500k^2+1063k-9k=0

We add all the numbers together, and all the variables

-4500k^2+1054k=0

a = -4500; b = 1054; c = 0;
Δ = b2-4ac
Δ = 10542-4·(-4500)·0
Δ = 1110916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1110916}=1054$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1054)-1054}{2*-4500}=\frac{-2108}{-9000}
=527/2250
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1054)+1054}{2*-4500}=\frac{0}{-9000}
=0
$