1/4n-3+3/5n=9

Solution for 1/4n-3+3/5n=9 equation:

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!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

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
$