2/7k-9/2=5+7/6k

Solution for 2/7k-9/2=5+7/6k equation:

2/7k-9/2=5+7/6k

We move all terms to the left:

2/7k-9/2-(5+7/6k)=0


Domain of the equation: 7k!=0

k!=0/7

k!=0

k∈R



Domain of the equation: 6k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

2/7k-(7/6k+5)-9/2=0

We get rid of parentheses

2/7k-7/6k-5-9/2=0

We calculate fractions


(-2268k^2)/168k^2+48k/168k^2+(-196k)/168k^2-5=0

We multiply all the terms by the denominator


(-2268k^2)+48k+(-196k)-5*168k^2=0

Wy multiply elements

(-2268k^2)-840k^2+48k+(-196k)=0

We get rid of parentheses

-2268k^2-840k^2+48k-196k=0

We add all the numbers together, and all the variables

-3108k^2-148k=0

a = -3108; b = -148; c = 0;
Δ = b2-4ac
Δ = -1482-4·(-3108)·0
Δ = 21904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21904}=148$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-148)-148}{2*-3108}=\frac{0}{-6216}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-148)+148}{2*-3108}=\frac{296}{-6216}
=-1/21
$