x+x(x+5)=162

Solution for x+x(x+5)=162 equation:

x+x(x+5)=162

We move all terms to the left:

x+x(x+5)-(162)=0

We multiply parentheses

x^2+x+5x-162=0

We add all the numbers together, and all the variables

x^2+6x-162=0

a = 1; b = 6; c = -162;
Δ = b2-4ac
Δ = 62-4·1·(-162)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{19}}{2*1}=\frac{-6-6\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{19}}{2*1}=\frac{-6+6\sqrt{19}}{2}
$