-2/5k-3/5=-4+6/7k

Solution for -2/5k-3/5=-4+6/7k equation:

-2/5k-3/5=-4+6/7k

We move all terms to the left:

-2/5k-3/5-(-4+6/7k)=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

-2/5k-(6/7k-4)-3/5=0

We get rid of parentheses

-2/5k-6/7k+4-3/5=0

We calculate fractions


(-14k)/875k^2+(-750k)/875k^2+(-21k)/875k^2+4=0

We multiply all the terms by the denominator


(-14k)+(-750k)+(-21k)+4*875k^2=0

Wy multiply elements

3500k^2+(-14k)+(-750k)+(-21k)=0

We get rid of parentheses

3500k^2-14k-750k-21k=0

We add all the numbers together, and all the variables

3500k^2-785k=0

a = 3500; b = -785; c = 0;
Δ = b2-4ac
Δ = -7852-4·3500·0
Δ = 616225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{616225}=785$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-785)-785}{2*3500}=\frac{0}{7000}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-785)+785}{2*3500}=\frac{1570}{7000}
=157/700
$