Use the quadratic formula to solve for $x$. \[ 5 x^{2}+2 x-2=0 \] Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas. \[ x= \]

Step 1 ：Given the quadratic equation \(5x^{2}+2x-2=0\), we are asked to find the solutions for \(x\).

Step 2 ：We can use the quadratic formula, which is given by \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a\), \(b\), and \(c\) are coefficients of the quadratic equation \(ax^2 + bx + c = 0\).

Step 3 ：In this case, \(a = 5\), \(b = 2\), and \(c = -2\). We can substitute these values into the quadratic formula to find the solutions for \(x\).

Step 4 ：Calculating the discriminant \(D = b^2 - 4ac = 44\).

Step 5 ：Substituting \(a\), \(b\), and \(D\) into the quadratic formula, we get two solutions: \(x1 = 0.46\) and \(x2 = -0.86\).

Step 6 ：Final Answer: The solutions to the equation are \(x = \boxed{0.46}\) and \(x = \boxed{-0.86}\).