0=0.25x^2-0.5x-8

Solution for 0=0.25x^2-0.5x-8 equation:

0=0.25x^2-0.5x-8

We move all terms to the left:

0-(0.25x^2-0.5x-8)=0

We add all the numbers together, and all the variables

-(0.25x^2-0.5x-8)=0

We get rid of parentheses

-0.25x^2+0.5x+8=0

a = -0.25; b = 0.5; c = +8;
Δ = b2-4ac
Δ = 0.52-4·(-0.25)·8
Δ = 8.25
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{8.25}}{2*-0.25}=\frac{-0.5-\sqrt{8.25}}{-0.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{8.25}}{2*-0.25}=\frac{-0.5+\sqrt{8.25}}{-0.5}
$