1/2n-3/5=3/5n-5

Solution for 1/2n-3/5=3/5n-5 equation:

1/2n-3/5=3/5n-5

We move all terms to the left:

1/2n-3/5-(3/5n-5)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



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

n∈R


We get rid of parentheses

1/2n-3/5n+5-3/5=0

We calculate fractions


125n/250n^2+(-6n)/250n^2+(-6n)/250n^2+5=0

We multiply all the terms by the denominator


125n+(-6n)+(-6n)+5*250n^2=0

Wy multiply elements

1250n^2+125n+(-6n)+(-6n)=0

We get rid of parentheses

1250n^2+125n-6n-6n=0

We add all the numbers together, and all the variables

1250n^2+113n=0

a = 1250; b = 113; c = 0;
Δ = b2-4ac
Δ = 1132-4·1250·0
Δ = 12769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12769}=113$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(113)-113}{2*1250}=\frac{-226}{2500}
=-113/1250
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(113)+113}{2*1250}=\frac{0}{2500}
=0
$