1/4n+2/5n-5=-3

Solution for 1/4n+2/5n-5=-3 equation:

1/4n+2/5n-5=-3

We move all terms to the left:

1/4n+2/5n-5-(-3)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

1/4n+2/5n-2=0

We calculate fractions


5n/20n^2+8n/20n^2-2=0

We multiply all the terms by the denominator


5n+8n-2*20n^2=0

We add all the numbers together, and all the variables

13n-2*20n^2=0

Wy multiply elements

-40n^2+13n=0

a = -40; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-40)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-40}=\frac{-26}{-80}
=13/40
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-40}=\frac{0}{-80}
=0
$