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