Question

6x -$\frac{4x^{2}+1 }{2}$ = 2x - 6 Fiz as contas, mas o resultado não bate com o gabarito poderiam me ajudar?

Answer 1

$6x - (\frac{4x^2 + 1}{2}) = 2x - 6\\\\ 12x + \frac{(-4x^2 - 1)}{2} = 4x - 12 \\12x - 4x^2 - 1 = 4x - 12\\-4x^2 + 12x - 4x -1 + 12 = 0\\-4x^2 + 8x + 11 = 0\\\Delta = 8^2 - 4 \cdot (-4) \cdot 11\\\Delta = 64 + 16 \cdot 11\\\Delta = 64 + 176\\\Delta = 240\\\\x' = \frac{-8 - \sqrt240}{2 \cdot (-4)} = \boxed{\frac{-8-\sqrt240}{-8}}\\\\x" = \frac{-8 + \sqrt240}{2 \cdot (-4)} = \boxed{\frac{-8+\sqrt240}{-8}}$