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1/4n-3+3/5n=9
We move all terms to the left:
1/4n-3+3/5n-(9)=0
Domain of the equation: 4n!=0
n!=0/4
n!=0
n∈R
Domain of the equation: 5n!=0We add all the numbers together, and all the variables
n!=0/5
n!=0
n∈R
1/4n+3/5n-12=0
We calculate fractions
5n/20n^2+12n/20n^2-12=0
We multiply all the terms by the denominator
5n+12n-12*20n^2=0
We add all the numbers together, and all the variables
17n-12*20n^2=0
Wy multiply elements
-240n^2+17n=0
a = -240; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-240)·0
Δ = 289
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{289}=17$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-240}=\frac{-34}{-480} =17/240 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-240}=\frac{0}{-480} =0 $
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