x(2x+12)=54

Solution for x(2x+12)=54 equation:

x(2x+12)=54

We move all terms to the left:

x(2x+12)-(54)=0

We multiply parentheses

2x^2+12x-54=0

a = 2; b = 12; c = -54;
Δ = b2-4ac
Δ = 122-4·2·(-54)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-24}{2*2}=\frac{-36}{4}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+24}{2*2}=\frac{12}{4}
=3
$