x+5/3x+2=-4

Solution for x+5/3x+2=-4 equation:

x+5/3x+2=-4

We move all terms to the left:

x+5/3x+2-(-4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+5/3x+6=0

We multiply all the terms by the denominator


x*3x+6*3x+5=0

Wy multiply elements

3x^2+18x+5=0

a = 3; b = 18; c = +5;
Δ = b2-4ac
Δ = 182-4·3·5
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{66}}{2*3}=\frac{-18-2\sqrt{66}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{66}}{2*3}=\frac{-18+2\sqrt{66}}{6}
$