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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

X^2+X-42=0

a = 1; b = 1; c = -42;
Δ = b2-4ac
Δ = 12-4·1·(-42)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-13}{2*1}=\frac{-14}{2}
=-7
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+13}{2*1}=\frac{12}{2}
=6
$