-4/7k+-8/5=-4-8/5k

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

-4/7k+-8/5=-4-8/5k

We move all terms to the left:

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

We add all the numbers together, and all the variables

-4/7k-(-8/5k-4)-8/5=0

We get rid of parentheses

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

We calculate fractions


(-500k)/875k^2+56k/875k^2+(-56k)/875k^2+4=0

We multiply all the terms by the denominator


(-500k)+56k+(-56k)+4*875k^2=0

We add all the numbers together, and all the variables

56k+(-500k)+(-56k)+4*875k^2=0

Wy multiply elements

3500k^2+56k+(-500k)+(-56k)=0

We get rid of parentheses

3500k^2+56k-500k-56k=0

We add all the numbers together, and all the variables

3500k^2-500k=0

a = 3500; b = -500; c = 0;
Δ = b2-4ac
Δ = -5002-4·3500·0
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*3500}=\frac{0}{7000}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+500}{2*3500}=\frac{1000}{7000}
=1/7
$