3/2n-4/5=2/10n+5

Solution for 3/2n-4/5=2/10n+5 equation:

3/2n-4/5=2/10n+5

We move all terms to the left:

3/2n-4/5-(2/10n+5)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 10n+5)!=0

n∈R


We get rid of parentheses

3/2n-2/10n-5-4/5=0

We calculate fractions


(-80n^2)/500n^2+750n/500n^2+(-100n)/500n^2-5=0

We multiply all the terms by the denominator


(-80n^2)+750n+(-100n)-5*500n^2=0

Wy multiply elements

(-80n^2)-2500n^2+750n+(-100n)=0

We get rid of parentheses

-80n^2-2500n^2+750n-100n=0

We add all the numbers together, and all the variables

-2580n^2+650n=0

a = -2580; b = 650; c = 0;
Δ = b2-4ac
Δ = 6502-4·(-2580)·0
Δ = 422500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{422500}=650$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(650)-650}{2*-2580}=\frac{-1300}{-5160}
=65/258
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(650)+650}{2*-2580}=\frac{0}{-5160}
=0
$