-11/8+19/5n=5/2n-3

Solution for -11/8+19/5n=5/2n-3 equation:

-11/8+19/5n=5/2n-3

We move all terms to the left:

-11/8+19/5n-(5/2n-3)=0


Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R



Domain of the equation: 2n-3)!=0

n∈R


We get rid of parentheses

19/5n-5/2n+3-11/8=0

We calculate fractions


(-220n^2)/640n^2+2432n/640n^2+(-1600n)/640n^2+3=0

We multiply all the terms by the denominator


(-220n^2)+2432n+(-1600n)+3*640n^2=0

Wy multiply elements

(-220n^2)+1920n^2+2432n+(-1600n)=0

We get rid of parentheses

-220n^2+1920n^2+2432n-1600n=0

We add all the numbers together, and all the variables

1700n^2+832n=0

a = 1700; b = 832; c = 0;
Δ = b2-4ac
Δ = 8322-4·1700·0
Δ = 692224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{692224}=832$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(832)-832}{2*1700}=\frac{-1664}{3400}
=-208/425
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(832)+832}{2*1700}=\frac{0}{3400}
=0
$