3x+9/2x+6=-2

Solution for 3x+9/2x+6=-2 equation:

3x+9/2x+6=-2

We move all terms to the left:

3x+9/2x+6-(-2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+9/2x+8=0

We multiply all the terms by the denominator


3x*2x+8*2x+9=0

Wy multiply elements

6x^2+16x+9=0

a = 6; b = 16; c = +9;
Δ = b2-4ac
Δ = 162-4·6·9
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{10}}{2*6}=\frac{-16-2\sqrt{10}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{10}}{2*6}=\frac{-16+2\sqrt{10}}{12}
$