0=0.5x^2+1.25x-0.1

Solution for 0=0.5x^2+1.25x-0.1 equation:

0=0.5x^2+1.25x-0.1

We move all terms to the left:

0-(0.5x^2+1.25x-0.1)=0

We add all the numbers together, and all the variables

-(0.5x^2+1.25x-0.1)=0

We get rid of parentheses

-0.5x^2-1.25x+0.1=0

a = -0.5; b = -1.25; c = +0.1;
Δ = b2-4ac
Δ = -1.252-4·(-0.5)·0.1
Δ = 1.7625
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{-(-1.25)-\sqrt{1.7625}}{2*-0.5}=\frac{1.25-\sqrt{1.7625}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.25)+\sqrt{1.7625}}{2*-0.5}=\frac{1.25+\sqrt{1.7625}}{-1}
$