3x(x+2)=5/9

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

3x(x+2)=5/9

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

3x^2+6x-(+5/9)=0

We get rid of parentheses

3x^2+6x-5/9=0

We multiply all the terms by the denominator


3x^2*9+6x*9-5=0

Wy multiply elements

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}
$