0.5x^2-7x+2=0

Solution for 0.5x^2-7x+2=0 equation:

0.5x^2-7x+2=0

a = 0.5; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·0.5·2
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3\sqrt{5}}{2*0.5}=\frac{7-3\sqrt{5}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3\sqrt{5}}{2*0.5}=\frac{7+3\sqrt{5}}{1}
$