2x+2/3x+8=-16

Solution for 2x+2/3x+8=-16 equation:

2x+2/3x+8=-16

We move all terms to the left:

2x+2/3x+8-(-16)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x+2/3x+24=0

We multiply all the terms by the denominator


2x*3x+24*3x+2=0

Wy multiply elements

6x^2+72x+2=0

a = 6; b = 72; c = +2;
Δ = b2-4ac
Δ = 722-4·6·2
Δ = 5136
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:

$\sqrt{\Delta}=\sqrt{5136}=\sqrt{16*321}=\sqrt{16}*\sqrt{321}=4\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-4\sqrt{321}}{2*6}=\frac{-72-4\sqrt{321}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+4\sqrt{321}}{2*6}=\frac{-72+4\sqrt{321}}{12}
$