0.5(x-6)(x+2)=0

Solution for 0.5(x-6)(x+2)=0 equation:

0.5(x-6)(x+2)=0

We multiply parentheses ..

0.5(+x^2+2x-6x-12)=0

We multiply parentheses

0.5x^2+x-3x-6=0

We add all the numbers together, and all the variables

0.5x^2-2x-6=0

a = 0.5; b = -2; c = -6;
Δ = b2-4ac
Δ = -22-4·0.5·(-6)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4}{2*0.5}=\frac{-2}{1}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4}{2*0.5}=\frac{6}{1}
=6
$