0,2x2 + 3x - 20 = 0

To solve the quadratic equation \(0.2x^2 + 3x - 20 = 0\), we can use the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

where \(a = 0.2\), \(b = 3\), and \(c = -20\).

First, let's calculate the discriminant (\(b^2 - 4ac\)):

\[ b^2 = 3^2 = 9 \] \[ 4ac = 4 \cdot 0.2 \cdot (-20) = -16 \]

Now, substituting into the equation:

\[ b^2 - 4ac = 9 - (-16) = 9 + 16 = 25 \]

Now plug in the values into the quadratic formula:

\[ x = \frac{-3 \pm \sqrt{25}}{2 \cdot 0.2} \] \[ x = \frac{-3 \pm 5}{0.4} \]

Now, calculate the two possible values for \(x\):

1. \(x = \frac{-3 + 5}{0.4} = \frac{2}{0.4} = 5\)
2. \(x = \frac{-3 - 5}{0.4} = \frac{-8}{0.4} = -20\)

Thus, the solutions to the equation \(0.2x^2 + 3x - 20 = 0\) are:

\[ x = 5 \quad \text{and} \quad x = -20 \]