4/7k-9/5=3-9/5k

Solution for 4/7k-9/5=3-9/5k equation:

4/7k-9/5=3-9/5k

We move all terms to the left:

4/7k-9/5-(3-9/5k)=0


Domain of the equation: 7k!=0

k!=0/7

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

4/7k-(-9/5k+3)-9/5=0

We get rid of parentheses

4/7k+9/5k-3-9/5=0

We calculate fractions


500k/875k^2+63k/875k^2+(-63k)/875k^2-3=0

We multiply all the terms by the denominator


500k+63k+(-63k)-3*875k^2=0

We add all the numbers together, and all the variables

563k+(-63k)-3*875k^2=0

Wy multiply elements

-2625k^2+563k+(-63k)=0

We get rid of parentheses

-2625k^2+563k-63k=0

We add all the numbers together, and all the variables

-2625k^2+500k=0

a = -2625; b = 500; c = 0;
Δ = b2-4ac
Δ = 5002-4·(-2625)·0
Δ = 250000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{250000}=500$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(500)-500}{2*-2625}=\frac{-1000}{-5250}
=4/21
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(500)+500}{2*-2625}=\frac{0}{-5250}
=0
$