3x(9-9x)=4/3

Solution for 3x(9-9x)=4/3 equation:

3x(9-9x)=4/3

We move all terms to the left:

3x(9-9x)-(4/3)=0

We add all the numbers together, and all the variables

3x(-9x+9)-(+4/3)=0

We multiply parentheses

-27x^2+27x-(+4/3)=0

We get rid of parentheses

-27x^2+27x-4/3=0

We multiply all the terms by the denominator


-27x^2*3+27x*3-4=0

Wy multiply elements

-81x^2+81x-4=0

a = -81; b = 81; c = -4;
Δ = b2-4ac
Δ = 812-4·(-81)·(-4)
Δ = 5265
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:

$\sqrt{\Delta}=\sqrt{5265}=\sqrt{81*65}=\sqrt{81}*\sqrt{65}=9\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-9\sqrt{65}}{2*-81}=\frac{-81-9\sqrt{65}}{-162}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+9\sqrt{65}}{2*-81}=\frac{-81+9\sqrt{65}}{-162}
$