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

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

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

We move all terms to the left:

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


Domain of the equation: 5k!=0

k!=0/5

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

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

We get rid of parentheses

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

We calculate fractions


28k/875k^2+(-625k)/875k^2+(-7k)/875k^2+4=0

We multiply all the terms by the denominator


28k+(-625k)+(-7k)+4*875k^2=0

Wy multiply elements

3500k^2+28k+(-625k)+(-7k)=0

We get rid of parentheses

3500k^2+28k-625k-7k=0

We add all the numbers together, and all the variables

3500k^2-604k=0

a = 3500; b = -604; c = 0;
Δ = b2-4ac
Δ = -6042-4·3500·0
Δ = 364816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{364816}=604$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-604)-604}{2*3500}=\frac{0}{7000}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-604)+604}{2*3500}=\frac{1208}{7000}
=151/875
$