2х(2)-12х+10=0

To solve the quadratic equation \(2x^2 - 12x + 10 = 0\), we can use the quadratic formula:

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

where \(a = 2\), \(b = -12\), and \(c = 10\).

1. Calculate the discriminant (\(b^2 - 4ac\)):

\[ b^2 = (-12)^2 = 144 \] \[ 4ac = 4 \cdot 2 \cdot 10 = 80 \] \[ b^2 - 4ac = 144 - 80 = 64 \]

2. Calculate the roots:

Now, substitute the values into the quadratic formula:

\[ x = \frac{-(-12) \pm \sqrt{64}}{2 \cdot 2} \] \[ x = \frac{12 \pm 8}{4} \]

This gives us two possible solutions:

\[ x_1 = \frac{12 + 8}{4} = \frac{20}{4} = 5 \] \[ x_2 = \frac{12 - 8}{4} = \frac{4}{4} = 1 \]

3. Final solutions:

The solutions to the equation \(2x^2 - 12x + 10 = 0\) are:

\[ x = 5 \quad \text{and} \quad x = 1 \]