x(x-2)+(2x+8)+10=60

Solution for x(x-2)+(2x+8)+10=60 equation:

x(x-2)+(2x+8)+10=60

We move all terms to the left:

x(x-2)+(2x+8)+10-(60)=0

We add all the numbers together, and all the variables

x(x-2)+(2x+8)-50=0

We multiply parentheses

x^2-2x+(2x+8)-50=0

We get rid of parentheses

x^2-2x+2x+8-50=0

We add all the numbers together, and all the variables

x^2-42=0

a = 1; b = 0; c = -42;
Δ = b2-4ac
Δ = 02-4·1·(-42)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*1}=\frac{0-2\sqrt{42}}{2}
=-\frac{2\sqrt{42}}{2}
=-\sqrt{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*1}=\frac{0+2\sqrt{42}}{2}
=\frac{2\sqrt{42}}{2}
=\sqrt{42}
$