3x(x+6)=27

Solution for 3x(x+6)=27 equation:

3x(x+6)=27

We move all terms to the left:

3x(x+6)-(27)=0

We multiply parentheses

3x^2+18x-27=0

a = 3; b = 18; c = -27;
Δ = b2-4ac
Δ = 182-4·3·(-27)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18\sqrt{2}}{2*3}=\frac{-18-18\sqrt{2}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18\sqrt{2}}{2*3}=\frac{-18+18\sqrt{2}}{6}
$