17х-6-5х2=0

To solve the equation \(17x - 6 - 5x^2 = 0\), we first need to rearrange the terms: \[5x^2 + 17x - 6 = 0\] Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula: The quadratic formula is given by: \[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\] In our equation, \(a = 5\), \(b = 17\), and \(c = -6\). Plugging these values into the formula, we get: \[x = \frac{-17 \pm \sqrt{17^2 - 4*5*(-6)}}{2*5}\] \[x = \frac{-17 \pm \sqrt{289 + 120}}{10}\] \[x = \frac{-17 \pm \sqrt{409}}{10}\] \[x = \frac{-17 \pm 19}{10}\] Therefore, the solutions are: \[x_1 = \frac{-17 + 19}{10} = \frac{2}{10} = 0.2\] \[x_2 = \frac{-17 - 19}{10} = \frac{-36}{10} = -3.6\] So, the solutions to the equation \(17x - 6 - 5x^2 = 0\) are \(x = 0.2\) and \(x = -3.6\).