\( -5 x^{2}+6 x-2=0 \) Write one exact, simplified solution in each box. You can add or remove boxes. If a solution not a real number, write it in the form \( \mathrm{a}+\mathrm{bi} \) or \( \mathrm{a}-\mathrm{bi} \), where a and b are real numbers. +

To solve the quadratic equation \( -5 x^{2}+6 x-2=0 \), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Here, \( a = -5 \), \( b = 6 \), and \( c = -2 \). Plugging these values into the formula gives: 1. Calculate the discriminant: \[ b^2 - 4ac = 6^2 - 4(-5)(-2) = 36 - 40 = -4 \] Since the discriminant is negative, the solutions will be complex numbers. 2. Apply the quadratic formula: \[ x = \frac{-6 \pm \sqrt{-4}}{2(-5)} = \frac{-6 \pm 2i}{-10} \] 3. Simplify: \[ x = \frac{6 \mp 2i}{10} = \frac{3 \mp i}{5} \] Thus, the two solutions are: \(\frac{3+i}{5}\) and \(\frac{3-i}{5}\).