18=6x+x(x+3)

Solution for 18=6x+x(x+3) equation:

18=6x+x(x+3)

We move all terms to the left:

18-(6x+x(x+3))=0


We calculate terms in parentheses: -(6x+x(x+3)), so:

6x+x(x+3)

We multiply parentheses

x^2+6x+3x

We add all the numbers together, and all the variables

x^2+9x

Back to the equation:

-(x^2+9x)


We get rid of parentheses

-x^2-9x+18=0

We add all the numbers together, and all the variables

-1x^2-9x+18=0

a = -1; b = -9; c = +18;
Δ = b2-4ac
Δ = -92-4·(-1)·18
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{17}}{2*-1}=\frac{9-3\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{17}}{2*-1}=\frac{9+3\sqrt{17}}{-2}
$