Determine the number and type of solutions of the given quadratic equation. Do not solve. 
$-4x^2+4x+5=0$

• A. 2 real solutions 
• B. 1 real solution 
• C. 2 imaginary solutions 

Answer: (A)

Verified step by step guidance

1. Identify the coefficients of the quadratic equation in the form \(ax^2 + bx + c = 0\). Here, \(a = -4\), \(b = 4\), and \(c = 5\).
2. Calculate the discriminant using the formula \(\Delta = b^2 - 4ac\) to determine the nature of the solutions.
3. Substitute the values of \(a\), \(b\), and \(c\) into the discriminant formula: \(\Delta = (4)^2 - 4 \times (-4) \times 5\).
4. Simplify the expression for the discriminant to find its value without fully calculating it.
5. Interpret the discriminant: if \(\Delta > 0\), there are 2 real solutions; if \(\Delta = 0\), there is 1 real solution; if \(\Delta < 0\), there are 2 imaginary solutions.