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

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

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

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We calculate fractions


(-15n)/6n^2+10n/6n^2-10=0

We multiply all the terms by the denominator


(-15n)+10n-10*6n^2=0

We add all the numbers together, and all the variables

10n+(-15n)-10*6n^2=0

Wy multiply elements

-60n^2+10n+(-15n)=0

We get rid of parentheses

-60n^2+10n-15n=0

We add all the numbers together, and all the variables

-60n^2-5n=0

a = -60; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-60)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-60}=\frac{0}{-120}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-60}=\frac{10}{-120}
=-1/12
$