x(x-2)+x+2x+8=60

Solution for x(x-2)+x+2x+8=60 equation:

x(x-2)+x+2x+8=60

We move all terms to the left:

x(x-2)+x+2x+8-(60)=0

We add all the numbers together, and all the variables

3x+x(x-2)-52=0

We multiply parentheses

x^2+3x-2x-52=0

We add all the numbers together, and all the variables

x^2+x-52=0

a = 1; b = 1; c = -52;
Δ = b2-4ac
Δ = 12-4·1·(-52)
Δ = 209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{209}}{2*1}=\frac{-1-\sqrt{209}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{209}}{2*1}=\frac{-1+\sqrt{209}}{2}
$