x(9+x)=162

Solution for x(9+x)=162 equation:

x(9+x)=162

We move all terms to the left:

x(9+x)-(162)=0

We add all the numbers together, and all the variables

x(x+9)-162=0

We multiply parentheses

x^2+9x-162=0

a = 1; b = 9; c = -162;
Δ = b2-4ac
Δ = 92-4·1·(-162)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-27}{2*1}=\frac{-36}{2}
=-18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+27}{2*1}=\frac{18}{2}
=9
$