.5x2-8x+2=0

Solution for .5x2-8x+2=0 equation:

.5x^2-8x+2=0

a = .5; b = -8; c = +2;
Δ = b2-4ac
Δ = -82-4·.5·2
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{15}}{2*.5}=\frac{8-2\sqrt{15}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{15}}{2*.5}=\frac{8+2\sqrt{15}}{1}
$