2=x(3+x)

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

2=x(3+x)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


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

x(x+3)

We multiply parentheses

x^2+3x

Back to the equation:

-(x^2+3x)


We get rid of parentheses

-x^2-3x+2=0

We add all the numbers together, and all the variables

-1x^2-3x+2=0

a = -1; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-1)·2
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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