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

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

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

We move all terms to the left:

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


Domain of the equation: 9k!=0

k!=0/9

k!=0

k∈R



Domain of the equation: 7k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


441k^2/1575k^2+700k/1575k^2+(-1125k)/1575k^2+7=0

We multiply all the terms by the denominator


441k^2+700k+(-1125k)+7*1575k^2=0

Wy multiply elements

441k^2+11025k^2+700k+(-1125k)=0

We get rid of parentheses

441k^2+11025k^2+700k-1125k=0

We add all the numbers together, and all the variables

11466k^2-425k=0

a = 11466; b = -425; c = 0;
Δ = b2-4ac
Δ = -4252-4·11466·0
Δ = 180625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{180625}=425$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-425)-425}{2*11466}=\frac{0}{22932}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-425)+425}{2*11466}=\frac{850}{22932}
=425/11466
$