/3k-14=7k+2

Solution for /3k-14=7k+2 equation:

/3k-14=7k+2

We move all terms to the left:

/3k-14-(7k+2)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R


We get rid of parentheses

/3k-7k-2-14=0

We multiply all the terms by the denominator


-7k*3k-2*3k-14*3k+=0

We add all the numbers together, and all the variables

-7k*3k-2*3k-14*3k=0

Wy multiply elements

-21k^2-6k-42k=0

We add all the numbers together, and all the variables

-21k^2-48k=0

a = -21; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·(-21)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*-21}=\frac{0}{-42}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*-21}=\frac{96}{-42}
=-2+2/7
$