2/5n+1/10=1/2n+2

Solution for 2/5n+1/10=1/2n+2 equation:

2/5n+1/10=1/2n+2

We move all terms to the left:

2/5n+1/10-(1/2n+2)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 2n+2)!=0

n∈R


We get rid of parentheses

2/5n-1/2n-2+1/10=0

We calculate fractions


20n^2/100n^2+40n/100n^2+(-50n)/100n^2-2=0

We multiply all the terms by the denominator


20n^2+40n+(-50n)-2*100n^2=0

Wy multiply elements

20n^2-200n^2+40n+(-50n)=0

We get rid of parentheses

20n^2-200n^2+40n-50n=0

We add all the numbers together, and all the variables

-180n^2-10n=0

a = -180; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-180)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-180}=\frac{0}{-360}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-180}=\frac{20}{-360}
=-1/18
$