n+4/2n+8=0

Solution for n+4/2n+8=0 equation:

n+4/2n+8=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We multiply all the terms by the denominator


n*2n+8*2n+4=0

Wy multiply elements

2n^2+16n+4=0

a = 2; b = 16; c = +4;
Δ = b2-4ac
Δ = 162-4·2·4
Δ = 224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{14}}{2*2}=\frac{-16-4\sqrt{14}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{14}}{2*2}=\frac{-16+4\sqrt{14}}{4}
$