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

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

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

We move all terms to the left:

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


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

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

3n-(5(2/5n+10))+30=0

We multiply all the terms by the denominator


3n*5n+30*5n+10))-(5(2+10))=0

We add all the numbers together, and all the variables

3n*5n+30*5n+10))-(512)=0

We add all the numbers together, and all the variables

3n*5n+30*5n=0

Wy multiply elements

15n^2+150n=0

a = 15; b = 150; c = 0;
Δ = b2-4ac
Δ = 1502-4·15·0
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-150}{2*15}=\frac{-300}{30}
=-10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+150}{2*15}=\frac{0}{30}
=0
$