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

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

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

We move all terms to the left:

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


Domain of the equation: 7k!=0

k!=0/7

k!=0

k∈R



Domain of the equation: 4k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-560k^2)/252k^2+108k/252k^2+189k/252k^2+2=0

We multiply all the terms by the denominator


(-560k^2)+108k+189k+2*252k^2=0

We add all the numbers together, and all the variables

(-560k^2)+297k+2*252k^2=0

Wy multiply elements

(-560k^2)+504k^2+297k=0

We get rid of parentheses

-560k^2+504k^2+297k=0

We add all the numbers together, and all the variables

-56k^2+297k=0

a = -56; b = 297; c = 0;
Δ = b2-4ac
Δ = 2972-4·(-56)·0
Δ = 88209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{88209}=297$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(297)-297}{2*-56}=\frac{-594}{-112}
=5+17/56
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(297)+297}{2*-56}=\frac{0}{-112}
=0
$