2/5n+5/6n=37/40

Solution for 2/5n+5/6n=37/40 equation:

2/5n+5/6n=37/40

We move all terms to the left:

2/5n+5/6n-(37/40)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R


We add all the numbers together, and all the variables

2/5n+5/6n-(+37/40)=0

We get rid of parentheses

2/5n+5/6n-37/40=0

We calculate fractions


(-6660n^2)/4800n^2+1920n/4800n^2+4000n/4800n^2=0

We multiply all the terms by the denominator


(-6660n^2)+1920n+4000n=0

We add all the numbers together, and all the variables

(-6660n^2)+5920n=0

We get rid of parentheses

-6660n^2+5920n=0

a = -6660; b = 5920; c = 0;
Δ = b2-4ac
Δ = 59202-4·(-6660)·0
Δ = 35046400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{35046400}=5920$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5920)-5920}{2*-6660}=\frac{-11840}{-13320}
=8/9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5920)+5920}{2*-6660}=\frac{0}{-13320}
=0
$