x+2/4x+8=-3

Solution for x+2/4x+8=-3 equation:

x+2/4x+8=-3

We move all terms to the left:

x+2/4x+8-(-3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+2/4x+11=0

We multiply all the terms by the denominator


x*4x+11*4x+2=0

Wy multiply elements

4x^2+44x+2=0

a = 4; b = 44; c = +2;
Δ = b2-4ac
Δ = 442-4·4·2
Δ = 1904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1904}=\sqrt{16*119}=\sqrt{16}*\sqrt{119}=4\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{119}}{2*4}=\frac{-44-4\sqrt{119}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{119}}{2*4}=\frac{-44+4\sqrt{119}}{8}
$