20=0.1x^2-0.5x-5

Solution for 20=0.1x^2-0.5x-5 equation:

20=0.1x^2-0.5x-5

We move all terms to the left:

20-(0.1x^2-0.5x-5)=0

We get rid of parentheses

-0.1x^2+0.5x+5+20=0

We add all the numbers together, and all the variables

-0.1x^2+0.5x+25=0

a = -0.1; b = 0.5; c = +25;
Δ = b2-4ac
Δ = 0.52-4·(-0.1)·25
Δ = 10.25
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{10.25}}{2*-0.1}=\frac{-0.5-\sqrt{10.25}}{-0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{10.25}}{2*-0.1}=\frac{-0.5+\sqrt{10.25}}{-0.2}
$