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

Solution for (7)/(10)n+(3)/(2)=(3)/(5)n+2 equation:

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

We move all terms to the left:

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


Domain of the equation: 10n!=0

n!=0/10

n!=0

n∈R



Domain of the equation: 5n+2)!=0

n∈R


We get rid of parentheses

7/10n-3/5n-2+3/2=0

We calculate fractions


750n^2/200n^2+140n/200n^2+(-120n)/200n^2-2=0

We multiply all the terms by the denominator


750n^2+140n+(-120n)-2*200n^2=0

Wy multiply elements

750n^2-400n^2+140n+(-120n)=0

We get rid of parentheses

750n^2-400n^2+140n-120n=0

We add all the numbers together, and all the variables

350n^2+20n=0

a = 350; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·350·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*350}=\frac{-40}{700}
=-2/35
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*350}=\frac{0}{700}
=0
$