x(4+x*2)=18

Solution for x(4+x*2)=18 equation:

x(4+x*2)=18

We move all terms to the left:

x(4+x*2)-(18)=0

We add all the numbers together, and all the variables

x(x*2+4)-18=0

We multiply parentheses

2x^2+4x-18=0

a = 2; b = 4; c = -18;
Δ = b2-4ac
Δ = 42-4·2·(-18)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{10}}{2*2}=\frac{-4-4\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{10}}{2*2}=\frac{-4+4\sqrt{10}}{4}
$