1/2k-6=3/7k+4

Solution for 1/2k-6=3/7k+4 equation:

1/2k-6=3/7k+4

We move all terms to the left:

1/2k-6-(3/7k+4)=0


Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R



Domain of the equation: 7k+4)!=0

k∈R


We get rid of parentheses

1/2k-3/7k-4-6=0

We calculate fractions


7k/14k^2+(-6k)/14k^2-4-6=0

We add all the numbers together, and all the variables

7k/14k^2+(-6k)/14k^2-10=0

We multiply all the terms by the denominator


7k+(-6k)-10*14k^2=0

Wy multiply elements

-140k^2+7k+(-6k)=0

We get rid of parentheses

-140k^2+7k-6k=0

We add all the numbers together, and all the variables

-140k^2+k=0

a = -140; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-140)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-140}=\frac{-2}{-280}
=1/140
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-140}=\frac{0}{-280}
=0
$