1/4n+10=3/2n

Solution for 1/4n+10=3/2n equation:

1/4n+10=3/2n

We move all terms to the left:

1/4n+10-(3/2n)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 2n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

1/4n-(+3/2n)+10=0

We get rid of parentheses

1/4n-3/2n+10=0

We calculate fractions


2n/8n^2+(-12n)/8n^2+10=0

We multiply all the terms by the denominator


2n+(-12n)+10*8n^2=0

Wy multiply elements

80n^2+2n+(-12n)=0

We get rid of parentheses

80n^2+2n-12n=0

We add all the numbers together, and all the variables

80n^2-10n=0

a = 80; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·80·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*80}=\frac{0}{160}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*80}=\frac{20}{160}
=1/8
$