x(3+2x)=54

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

x(3+2x)=54

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(2x+3)-54=0

We multiply parentheses

2x^2+3x-54=0

a = 2; b = 3; c = -54;
Δ = b2-4ac
Δ = 32-4·2·(-54)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-21}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+21}{2*2}=\frac{18}{4}
=4+1/2
$