3=x(4+x)

Solution for 3=x(4+x) equation:

3=x(4+x)

We move all terms to the left:

3-(x(4+x))=0

We add all the numbers together, and all the variables

-(x(x+4))+3=0


We calculate terms in parentheses: -(x(x+4)), so:

x(x+4)

We multiply parentheses

x^2+4x

Back to the equation:

-(x^2+4x)


We get rid of parentheses

-x^2-4x+3=0

We add all the numbers together, and all the variables

-1x^2-4x+3=0

a = -1; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·(-1)·3
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{7}}{2*-1}=\frac{4-2\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{7}}{2*-1}=\frac{4+2\sqrt{7}}{-2}
$