0,5x^2-4x=6

Solution for 0,5x^2-4x=6 equation:

0.5x^2-4x=6

We move all terms to the left:

0.5x^2-4x-(6)=0

a = 0.5; b = -4; c = -6;
Δ = b2-4ac
Δ = -42-4·0.5·(-6)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{7}}{2*0.5}=\frac{4-2\sqrt{7}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{7}}{2*0.5}=\frac{4+2\sqrt{7}}{1}
$