(5)/(6)n-(7)/(12)=-(3)/(4)n=(13)/(6)

Solution for (5)/(6)n-(7)/(12)=-(3)/(4)n=(13)/(6) equation:

(5)/(6)n-(7)/(12)=-(3)/(4)n=(13)/(6)

We move all terms to the left:

(5)/(6)n-(7)/(12)-(-(3)/(4)n)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R



Domain of the equation: 4n)!=0

n!=0/1

n!=0

n∈R


We get rid of parentheses

5/6n+3/4n-7/12=0

We calculate fractions


(-672n^2)/288n^2+240n/288n^2+216n/288n^2=0

We multiply all the terms by the denominator


(-672n^2)+240n+216n=0

We add all the numbers together, and all the variables

(-672n^2)+456n=0

We get rid of parentheses

-672n^2+456n=0

a = -672; b = 456; c = 0;
Δ = b2-4ac
Δ = 4562-4·(-672)·0
Δ = 207936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{207936}=456$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(456)-456}{2*-672}=\frac{-912}{-1344}
=19/28
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(456)+456}{2*-672}=\frac{0}{-1344}
=0
$