-3/5k+2/5=8-5/7k

Solution for -3/5k+2/5=8-5/7k equation:

-3/5k+2/5=8-5/7k

We move all terms to the left:

-3/5k+2/5-(8-5/7k)=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

-3/5k-(-5/7k+8)+2/5=0

We get rid of parentheses

-3/5k+5/7k-8+2/5=0

We calculate fractions


(-21k)/875k^2+625k/875k^2+14k/875k^2-8=0

We multiply all the terms by the denominator


(-21k)+625k+14k-8*875k^2=0

We add all the numbers together, and all the variables

639k+(-21k)-8*875k^2=0

Wy multiply elements

-7000k^2+639k+(-21k)=0

We get rid of parentheses

-7000k^2+639k-21k=0

We add all the numbers together, and all the variables

-7000k^2+618k=0

a = -7000; b = 618; c = 0;
Δ = b2-4ac
Δ = 6182-4·(-7000)·0
Δ = 381924
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{381924}=618$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(618)-618}{2*-7000}=\frac{-1236}{-14000}
=309/3500
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(618)+618}{2*-7000}=\frac{0}{-14000}
=0
$