2x^2+4x-1=0,5

Solution for 2x^2+4x-1=0,5 equation:

2x^2+4x-1=0.5

We move all terms to the left:

2x^2+4x-1-(0.5)=0

We add all the numbers together, and all the variables

2x^2+4x-1.5=0

a = 2; b = 4; c = -1.5;
Δ = b2-4ac
Δ = 42-4·2·(-1.5)
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*2}=\frac{-4-2\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{7}}{2*2}=\frac{-4+2\sqrt{7}}{4}
$