0=x^2-0.5x-8

Solution for 0=x^2-0.5x-8 equation:

0=x^2-0.5x-8

We move all terms to the left:

0-(x^2-0.5x-8)=0

We add all the numbers together, and all the variables

-(x^2-0.5x-8)=0

We get rid of parentheses

-x^2+0.5x+8=0

We add all the numbers together, and all the variables

-1x^2+0.5x+8=0

a = -1; b = 0.5; c = +8;
Δ = b2-4ac
Δ = 0.52-4·(-1)·8
Δ = 32.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.5)-\sqrt{32.25}}{2*-1}=\frac{-0.5-\sqrt{32.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{32.25}}{2*-1}=\frac{-0.5+\sqrt{32.25}}{-2}
$