3/4n+n=-3.8

Solution for 3/4n+n=-3.8 equation:

3/4n+n=-3.8

We move all terms to the left:

3/4n+n-(-3.8)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

n+3/4n+3.8=0

We multiply all the terms by the denominator


n*4n+(3.8)*4n+3=0

We multiply parentheses

n*4n+15.2n+3=0

Wy multiply elements

4n^2+15.2n+3=0

a = 4; b = 15.2; c = +3;
Δ = b2-4ac
Δ = 15.22-4·4·3
Δ = 183.04
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15.2)-\sqrt{183.04}}{2*4}=\frac{-15.2-\sqrt{183.04}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15.2)+\sqrt{183.04}}{2*4}=\frac{-15.2+\sqrt{183.04}}{8}
$