Given: $x + y = 6t$
Square both sides to get: $(x + y)^2 = (6t)^2$
Expand and simplify: $x^2 + 2xy + y^2 = 36t^2$

Also given: $xy = -7t^2$
Multiply both sides by 2 to get: $2xy = -14t^2$

We now have two equations:
$x^2 + 2xy + y^2 = 36t^2$
$2xy = -14t^2$

Subtract the bottom equation from the top equation to get: $x^2 + y^2 = 50t^2$

Our goal is to find the value of $\frac{(x^2 + y^2)}{t^2}$

Replace the numerator with its equivalent value to get: $\frac{50t^2}{t^2}$

Simplify to get: 50

Answer: C

Cheers,
Brent