0=10x^2+2x-0.5

Solution for 0=10x^2+2x-0.5 equation:

0=10x^2+2x-0.5

We move all terms to the left:

0-(10x^2+2x-0.5)=0

We add all the numbers together, and all the variables

-(10x^2+2x-0.5)=0

We get rid of parentheses

-10x^2-2x+0.5=0

a = -10; b = -2; c = +0.5;
Δ = b2-4ac
Δ = -22-4·(-10)·0.5
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{6}}{2*-10}=\frac{2-2\sqrt{6}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{6}}{2*-10}=\frac{2+2\sqrt{6}}{-20}
$