x*(6+x)=46

Solution for x*(6+x)=46 equation:

x(6+x)=46

We move all terms to the left:

x(6+x)-(46)=0

We add all the numbers together, and all the variables

x(x+6)-46=0

We multiply parentheses

x^2+6x-46=0

a = 1; b = 6; c = -46;
Δ = b2-4ac
Δ = 62-4·1·(-46)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{55}}{2*1}=\frac{-6-2\sqrt{55}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{55}}{2*1}=\frac{-6+2\sqrt{55}}{2}
$