0.5=x*2x+0.5/2

Solution for 0.5=x*2x+0.5/2 equation:

0.5=x*2x+0.5/2

We move all terms to the left:

0.5-(x*2x+0.5/2)=0

We add all the numbers together, and all the variables

-(+x*2x+0.5/2)+0.5=0

We get rid of parentheses

-x*2x+0.5-0.5/2=0

We multiply all the terms by the denominator


-(x*2x)*2-0.5+(0.5)*2=0

We add all the numbers together, and all the variables

-(+x*2x)*2-0.5+(0.5)*2=0

We add all the numbers together, and all the variables

-(+x*2x)*2+0.5=0

We multiply parentheses

-4x^2+0.5=0

a = -4; b = 0; c = +0.5;
Δ = b2-4ac
Δ = 02-4·(-4)·0.5
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2}}{2*-4}=\frac{0-2\sqrt{2}}{-8}
=-\frac{2\sqrt{2}}{-8}
=-\frac{\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2}}{2*-4}=\frac{0+2\sqrt{2}}{-8}
=\frac{2\sqrt{2}}{-8}
=\frac{\sqrt{2}}{-4}
$