x(3x+6)=272

Solution for x(3x+6)=272 equation:

x(3x+6)=272

We move all terms to the left:

x(3x+6)-(272)=0

We multiply parentheses

3x^2+6x-272=0

a = 3; b = 6; c = -272;
Δ = b2-4ac
Δ = 62-4·3·(-272)
Δ = 3300
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:

$\sqrt{\Delta}=\sqrt{3300}=\sqrt{100*33}=\sqrt{100}*\sqrt{33}=10\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10\sqrt{33}}{2*3}=\frac{-6-10\sqrt{33}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10\sqrt{33}}{2*3}=\frac{-6+10\sqrt{33}}{6}
$