6/7k-12=3/14k+15

Solution for 6/7k-12=3/14k+15 equation:

6/7k-12=3/14k+15

We move all terms to the left:

6/7k-12-(3/14k+15)=0


Domain of the equation: 7k!=0

k!=0/7

k!=0

k∈R



Domain of the equation: 14k+15)!=0

k∈R


We get rid of parentheses

6/7k-3/14k-15-12=0

We calculate fractions


84k/98k^2+(-21k)/98k^2-15-12=0

We add all the numbers together, and all the variables

84k/98k^2+(-21k)/98k^2-27=0

We multiply all the terms by the denominator


84k+(-21k)-27*98k^2=0

Wy multiply elements

-2646k^2+84k+(-21k)=0

We get rid of parentheses

-2646k^2+84k-21k=0

We add all the numbers together, and all the variables

-2646k^2+63k=0

a = -2646; b = 63; c = 0;
Δ = b2-4ac
Δ = 632-4·(-2646)·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-63}{2*-2646}=\frac{-126}{-5292}
=1/42
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*-2646}=\frac{0}{-5292}
=0
$