(x-8)(x+0.1)=0

Solution for (x-8)(x+0.1)=0 equation:

(x-8)(x+0.1)=0

We multiply parentheses ..

(+x^2+0.1x-8x-0.8)=0

We get rid of parentheses

x^2+0.1x-8x-0.8=0

We add all the numbers together, and all the variables

x^2-7.9x-0.8=0

a = 1; b = -7.9; c = -0.8;
Δ = b2-4ac
Δ = -7.92-4·1·(-0.8)
Δ = 65.61
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{-(-7.9)-\sqrt{65.61}}{2*1}=\frac{7.9-\sqrt{65.61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.9)+\sqrt{65.61}}{2*1}=\frac{7.9+\sqrt{65.61}}{2}
$