3x(x-3)=27

Solution for 3x(x-3)=27 equation:

3x(x-3)=27

We move all terms to the left:

3x(x-3)-(27)=0

We multiply parentheses

3x^2-9x-27=0

a = 3; b = -9; c = -27;
Δ = b2-4ac
Δ = -92-4·3·(-27)
Δ = 405
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:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9\sqrt{5}}{2*3}=\frac{9-9\sqrt{5}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9\sqrt{5}}{2*3}=\frac{9+9\sqrt{5}}{6}
$