Solve the equation $5 x^{2}+8 x-23=0$ Show your working clearly. Give your solutions correct to 3 significant figures. What is the positive solution?

Step 1 ：Given the quadratic equation: \(5x^2 + 8x - 23 = 0\)

Step 2 ：Use the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

Step 3 ：Substitute the values: \(a = 5\), \(b = 8\), and \(c = -23\)

Step 4 ：Calculate the discriminant: \(\Delta = b^2 - 4ac = 524\)

Step 5 ：Find the two possible solutions for x: \(x_1 = \frac{-8 + \sqrt{524}}{10}\) and \(x_2 = \frac{-8 - \sqrt{524}}{10}\)

Step 6 ：Calculate the values of \(x_1\) and \(x_2\): \(x_1 \approx 1.489\) and \(x_2 \approx -3.089\)

Step 7 ：\(\boxed{x \approx 1.489}\) is the positive solution