3(x+2)9x=5

Solution for 3(x+2)9x=5 equation:

3(x+2)9x=5

We move all terms to the left:

3(x+2)9x-(5)=0

We multiply parentheses

27x^2+54x-5=0

a = 27; b = 54; c = -5;
Δ = b2-4ac
Δ = 542-4·27·(-5)
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-24\sqrt{6}}{2*27}=\frac{-54-24\sqrt{6}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+24\sqrt{6}}{2*27}=\frac{-54+24\sqrt{6}}{54}
$