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

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

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

We move all terms to the left:

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


Domain of the equation: 7k!=0

k!=0/7

k!=0

k∈R



Domain of the equation: 3k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


378k^2/525k^2+(-300k)/525k^2+(-1225k)/525k^2+6=0

We multiply all the terms by the denominator


378k^2+(-300k)+(-1225k)+6*525k^2=0

Wy multiply elements

378k^2+3150k^2+(-300k)+(-1225k)=0

We get rid of parentheses

378k^2+3150k^2-300k-1225k=0

We add all the numbers together, and all the variables

3528k^2-1525k=0

a = 3528; b = -1525; c = 0;
Δ = b2-4ac
Δ = -15252-4·3528·0
Δ = 2325625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2325625}=1525$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1525)-1525}{2*3528}=\frac{0}{7056}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1525)+1525}{2*3528}=\frac{3050}{7056}
=1525/3528
$