0=0.03x^2+0.5x-8

Solution for 0=0.03x^2+0.5x-8 equation:

0=0.03x^2+0.5x-8

We move all terms to the left:

0-(0.03x^2+0.5x-8)=0

We add all the numbers together, and all the variables

-(0.03x^2+0.5x-8)=0

We get rid of parentheses

-0.03x^2-0.5x+8=0

a = -0.03; b = -0.5; c = +8;
Δ = b2-4ac
Δ = -0.52-4·(-0.03)·8
Δ = 1.21
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{1.21}}{2*-0.03}=\frac{0.5-\sqrt{1.21}}{-0.06}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{1.21}}{2*-0.03}=\frac{0.5+\sqrt{1.21}}{-0.06}
$