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 \(x = -3.6\).