Question

What are the exact solutions of x2 − 3x − 5 = 0?

Answer 1

`x^(2) - 3x - 5 = 0 \\ \\ \Delta = (-3)^(2) - 4 \cdot 1 \cdot (-5) = 9 + 20 = 29 \\ \\ √(\Delta ) = √(29) \\ \\ x_(1) = (3 - √(29) )/(2) \\ \\ x_(2) = (3+ √(29) )/(2) \\ \\ \boxed{x \in \left \lbrace (3 - √(29) )/(2) , (3 + √(29) )/(2) \right \rbrace }`