Solve the equation by using the quadiatic formula \( -5 x^{2}+x=-4 \)

First, let's rearrange the equation to standard form: \( -5x^2 + x + 4 = 0 \). Now, we can apply the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, \( a = -5 \), \( b = 1 \), and \( c = 4 \). Plugging in these values gives \( x = \frac{-1 \pm \sqrt{1^2 - 4(-5)(4)}}{2(-5)} \). Simplifying this further leads to \( x = \frac{-1 \pm \sqrt{1 + 80}}{-10} \), resulting in \( x = \frac{-1 \pm 9}{-10} \), giving you the solutions \( x = \frac{-10}{-10} = 1 \) and \( x = \frac{8}{-10} = -0.8 \). Now, let’s do a quick wrap-up: you can always check your solutions by plugging them back into the original equation to ensure both sides balance out. It’s like a little mathematical dance where both partners (your solutions) need to move harmoniously together. If you try \( x = 1 \) and \( x = -0.8 \), both satisfy the original equation, confirming you’ve hit the right moves!