3x(x-4)=27

Solution for 3x(x-4)=27 equation:

3x(x-4)=27

We move all terms to the left:

3x(x-4)-(27)=0

We multiply parentheses

3x^2-12x-27=0

a = 3; b = -12; c = -27;
Δ = b2-4ac
Δ = -122-4·3·(-27)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{13}}{2*3}=\frac{12-6\sqrt{13}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{13}}{2*3}=\frac{12+6\sqrt{13}}{6}
$