1/2n+5=31/4n-6

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Solution for 1/2n+5=31/4n-6 equation: 



1/2n+5=31/4n-6

We move all terms to the left:

1/2n+5-(31/4n-6)=0



Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R





Domain of the equation: 4n-6)!=0

n∈R



We get rid of parentheses

1/2n-31/4n+6+5=0

We calculate fractions


4n/8n^2+(-62n)/8n^2+6+5=0

We add all the numbers together, and all the variables

4n/8n^2+(-62n)/8n^2+11=0

We multiply all the terms by the denominator


4n+(-62n)+11*8n^2=0

Wy multiply elements

88n^2+4n+(-62n)=0

We get rid of parentheses

88n^2+4n-62n=0

We add all the numbers together, and all the variables

88n^2-58n=0

a = 88; b = -58; c = 0;
Δ = b2-4ac
Δ = -582-4·88·0
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$


$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-58}{2*88}=\frac{0}{176}
=0
$


$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+58}{2*88}=\frac{116}{176}
=29/44
$

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