The problem asks to solve the quadratic equation $\frac{x^2}{4} - x = 15$ for $x$.

1. Problem Description

The problem asks to solve the quadratic equation $\frac{x^2}{4} - x = 15$ for $x$.

2. Solution Steps

First, multiply both sides of the equation by 4 to eliminate the fraction:

$4(\frac{x^2}{4} - x) = 4(15)$

$x^2 - 4x = 60$

Next, subtract 60 from both sides to set the equation to zero:

$x^2 - 4x - 60 = 0$

Now, we can solve this quadratic equation by factoring. We are looking for two numbers that multiply to -60 and add to -

4. These numbers are -10 and

6. So, the equation can be factored as:

$(x - 10)(x + 6) = 0$

Setting each factor to zero, we get the two possible solutions for $x$:

$x - 10 = 0$ or $x + 6 = 0$

$x = 10$ or $x = -6$

Therefore, the solutions are $x = 10$ and $x = -6$.

3. Final Answer

10, -6