3/4n+10=5/6n

Solution for 3/4n+10=5/6n equation:

3/4n+10=5/6n

We move all terms to the left:

3/4n+10-(5/6n)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 6n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

3/4n-(+5/6n)+10=0

We get rid of parentheses

3/4n-5/6n+10=0

We calculate fractions


18n/24n^2+(-20n)/24n^2+10=0

We multiply all the terms by the denominator


18n+(-20n)+10*24n^2=0

Wy multiply elements

240n^2+18n+(-20n)=0

We get rid of parentheses

240n^2+18n-20n=0

We add all the numbers together, and all the variables

240n^2-2n=0

a = 240; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·240·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*240}=\frac{0}{480}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*240}=\frac{4}{480}
=1/120
$