n/5-3n/4n+5n/8=32

Solution for n/5-3n/4n+5n/8=32 equation:

n/5-3n/4n+5n/8=32

We move all terms to the left:

n/5-3n/4n+5n/8-(32)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We calculate fractions


256n^2/1280n+400n^2/1280n+(-960n)/1280n-32=0

We multiply all the terms by the denominator


256n^2+400n^2+(-960n)-32*1280n=0

We add all the numbers together, and all the variables

656n^2+(-960n)-32*1280n=0

Wy multiply elements

656n^2+(-960n)-40960n=0

We get rid of parentheses

656n^2-960n-40960n=0

We add all the numbers together, and all the variables

656n^2-41920n=0

a = 656; b = -41920; c = 0;
Δ = b2-4ac
Δ = -419202-4·656·0
Δ = 1757286400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1757286400}=41920$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41920)-41920}{2*656}=\frac{0}{1312}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41920)+41920}{2*656}=\frac{83840}{1312}
=63+37/41
$