X(x-2)+3x+8=60

Solution for X(x-2)+3x+8=60 equation:

X(X-2)+3X+8=60

We move all terms to the left:

X(X-2)+3X+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}
$