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-2/3n-2/5n=-22/15
We move all terms to the left:
-2/3n-2/5n-(-22/15)=0
Domain of the equation: 3n!=0
n!=0/3
n!=0
n∈R
Domain of the equation: 5n!=0We get rid of parentheses
n!=0/5
n!=0
n∈R
-2/3n-2/5n+22/15=0
We calculate fractions
1650n^2/225n^2+(-150n)/225n^2+(-90n)/225n^2=0
We multiply all the terms by the denominator
1650n^2+(-150n)+(-90n)=0
We get rid of parentheses
1650n^2-150n-90n=0
We add all the numbers together, and all the variables
1650n^2-240n=0
a = 1650; b = -240; c = 0;
Δ = b2-4ac
Δ = -2402-4·1650·0
Δ = 57600
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{57600}=240$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-240}{2*1650}=\frac{0}{3300} =0 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+240}{2*1650}=\frac{480}{3300} =8/55 $
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