9/2x+18+3x=-9

Solution for 9/2x+18+3x=-9 equation:

9/2x+18+3x=-9

We move all terms to the left:

9/2x+18+3x-(-9)=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+27=0

We multiply all the terms by the denominator


3x*2x+27*2x+9=0

Wy multiply elements

6x^2+54x+9=0

a = 6; b = 54; c = +9;
Δ = b2-4ac
Δ = 542-4·6·9
Δ = 2700
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:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-30\sqrt{3}}{2*6}=\frac{-54-30\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+30\sqrt{3}}{2*6}=\frac{-54+30\sqrt{3}}{12}
$