4/5n+2=2/3n-4

Solution for 4/5n+2=2/3n-4 equation:

4/5n+2=2/3n-4

We move all terms to the left:

4/5n+2-(2/3n-4)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 3n-4)!=0

n∈R


We get rid of parentheses

4/5n-2/3n+4+2=0

We calculate fractions


12n/15n^2+(-10n)/15n^2+4+2=0

We add all the numbers together, and all the variables

12n/15n^2+(-10n)/15n^2+6=0

We multiply all the terms by the denominator


12n+(-10n)+6*15n^2=0

Wy multiply elements

90n^2+12n+(-10n)=0

We get rid of parentheses

90n^2+12n-10n=0

We add all the numbers together, and all the variables

90n^2+2n=0

a = 90; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·90·0
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*90}=\frac{-4}{180}
=-1/45
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*90}=\frac{0}{180}
=0
$