5/2n=8/3n-15

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Solution for 5/2n=8/3n-15 equation:



5/2n=8/3n-15
We move all terms to the left:
5/2n-(8/3n-15)=0
Domain of the equation: 2n!=0
n!=0/2
n!=0
n∈R
Domain of the equation: 3n-15)!=0
n∈R
We get rid of parentheses
5/2n-8/3n+15=0
We calculate fractions
15n/6n^2+(-16n)/6n^2+15=0
We multiply all the terms by the denominator
15n+(-16n)+15*6n^2=0
Wy multiply elements
90n^2+15n+(-16n)=0
We get rid of parentheses
90n^2+15n-16n=0
We add all the numbers together, and all the variables
90n^2-1n=0
a = 90; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·90·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*90}=\frac{0}{180} =0 $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*90}=\frac{2}{180} =1/90 $

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