-11/8n+5/2n=-9

Solution for -11/8n+5/2n=-9 equation:

-11/8n+5/2n=-9

We move all terms to the left:

-11/8n+5/2n-(-9)=0


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R



Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

-11/8n+5/2n+9=0

We calculate fractions


(-22n)/16n^2+40n/16n^2+9=0

We multiply all the terms by the denominator


(-22n)+40n+9*16n^2=0

We add all the numbers together, and all the variables

40n+(-22n)+9*16n^2=0

Wy multiply elements

144n^2+40n+(-22n)=0

We get rid of parentheses

144n^2+40n-22n=0

We add all the numbers together, and all the variables

144n^2+18n=0

a = 144; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·144·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*144}=\frac{-36}{288}
=-1/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*144}=\frac{0}{288}
=0
$