-3/2k+4/7=1+3/7k

Solution for -3/2k+4/7=1+3/7k equation:

-3/2k+4/7=1+3/7k

We move all terms to the left:

-3/2k+4/7-(1+3/7k)=0


Domain of the equation: 2k!=0

k!=0/2

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

-3/2k-(3/7k+1)+4/7=0

We get rid of parentheses

-3/2k-3/7k-1+4/7=0

We calculate fractions


(-1029k)/686k^2+(-6k)/686k^2+8k/686k^2-1=0

We multiply all the terms by the denominator


(-1029k)+(-6k)+8k-1*686k^2=0

We add all the numbers together, and all the variables

8k+(-1029k)+(-6k)-1*686k^2=0

Wy multiply elements

-686k^2+8k+(-1029k)+(-6k)=0

We get rid of parentheses

-686k^2+8k-1029k-6k=0

We add all the numbers together, and all the variables

-686k^2-1027k=0

a = -686; b = -1027; c = 0;
Δ = b2-4ac
Δ = -10272-4·(-686)·0
Δ = 1054729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1054729}=1027$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1027)-1027}{2*-686}=\frac{0}{-1372}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1027)+1027}{2*-686}=\frac{2054}{-1372}
=-1+341/686
$