9(3-x)3=x2

Solution for 9(3-x)3=x2 equation:

9(3-x)3=x2

We move all terms to the left:

9(3-x)3-(x2)=0

We add all the numbers together, and all the variables

9(-1x+3)3-x2=0

We add all the numbers together, and all the variables

-1x^2+9(-1x+3)3=0

We multiply parentheses

-1x^2-27x+81=0

a = -1; b = -27; c = +81;
Δ = b2-4ac
Δ = -272-4·(-1)·81
Δ = 1053
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:

$\sqrt{\Delta}=\sqrt{1053}=\sqrt{81*13}=\sqrt{81}*\sqrt{13}=9\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-9\sqrt{13}}{2*-1}=\frac{27-9\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+9\sqrt{13}}{2*-1}=\frac{27+9\sqrt{13}}{-2}
$