x(x-2)+2x+2x+18=60

Solution for x(x-2)+2x+2x+18=60 equation:

x(x-2)+2x+2x+18=60

We move all terms to the left:

x(x-2)+2x+2x+18-(60)=0

We add all the numbers together, and all the variables

4x+x(x-2)-42=0

We multiply parentheses

x^2+4x-2x-42=0

We add all the numbers together, and all the variables

x^2+2x-42=0

a = 1; b = 2; c = -42;
Δ = b2-4ac
Δ = 22-4·1·(-42)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{43}}{2*1}=\frac{-2-2\sqrt{43}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{43}}{2*1}=\frac{-2+2\sqrt{43}}{2}
$