0,5*(x-5)*(x+1)=0

Solution for 0,5*(x-5)*(x+1)=0 equation:

0.5(x-5)(x+1)=0

We multiply parentheses ..

0.5(+x^2+x-5x-5)=0

We multiply parentheses

0.5x^2+0.5x-2.5x-2.5=0

We add all the numbers together, and all the variables

0.5x^2-2x-2.5=0

a = 0.5; b = -2; c = -2.5;
Δ = b2-4ac
Δ = -22-4·0.5·(-2.5)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-3}{2*0.5}=\frac{-1}{1}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+3}{2*0.5}=\frac{5}{1}
=5
$