54=2x(3x+9)

Solution for 54=2x(3x+9) equation:

54=2x(3x+9)

We move all terms to the left:

54-(2x(3x+9))=0


We calculate terms in parentheses: -(2x(3x+9)), so:

2x(3x+9)

We multiply parentheses

6x^2+18x

Back to the equation:

-(6x^2+18x)


We get rid of parentheses

-6x^2-18x+54=0

a = -6; b = -18; c = +54;
Δ = b2-4ac
Δ = -182-4·(-6)·54
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18\sqrt{5}}{2*-6}=\frac{18-18\sqrt{5}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18\sqrt{5}}{2*-6}=\frac{18+18\sqrt{5}}{-12}
$