3x(2x+2)=54

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

3x(2x+2)=54

We move all terms to the left:

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

We multiply parentheses

6x^2+6x-54=0

a = 6; b = 6; c = -54;
Δ = b2-4ac
Δ = 62-4·6·(-54)
Δ = 1332
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:

$\sqrt{\Delta}=\sqrt{1332}=\sqrt{36*37}=\sqrt{36}*\sqrt{37}=6\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{37}}{2*6}=\frac{-6-6\sqrt{37}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{37}}{2*6}=\frac{-6+6\sqrt{37}}{12}
$