X(x-2)=224

Solution for X(x-2)=224 equation:

X(X-2)=224

We move all terms to the left:

X(X-2)-(224)=0

We multiply parentheses

X^2-2X-224=0

a = 1; b = -2; c = -224;
Δ = b2-4ac
Δ = -22-4·1·(-224)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-30}{2*1}=\frac{-28}{2}
=-14
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+30}{2*1}=\frac{32}{2}
=16
$