1/2n+2/5n=-9/10

Solution for 1/2n+2/5n=-9/10 equation:

1/2n+2/5n=-9/10

We move all terms to the left:

1/2n+2/5n-(-9/10)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R



Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We get rid of parentheses

1/2n+2/5n+9/10=0

We calculate fractions


450n^2/100n^2+50n/100n^2+40n/100n^2=0

We multiply all the terms by the denominator


450n^2+50n+40n=0

We add all the numbers together, and all the variables

450n^2+90n=0

a = 450; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·450·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*450}=\frac{-180}{900}
=-1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*450}=\frac{0}{900}
=0
$