0=96-20x+0.86x^2

Solution for 0=96-20x+0.86x^2 equation:

0=96-20x+0.86x^2

We move all terms to the left:

0-(96-20x+0.86x^2)=0

We add all the numbers together, and all the variables

-(96-20x+0.86x^2)=0

We get rid of parentheses

-0.86x^2+20x-96=0

a = -0.86; b = 20; c = -96;
Δ = b2-4ac
Δ = 202-4·(-0.86)·(-96)
Δ = 69.76
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{-(20)-\sqrt{69.76}}{2*-0.86}=\frac{-20-\sqrt{69.76}}{-1.72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+\sqrt{69.76}}{2*-0.86}=\frac{-20+\sqrt{69.76}}{-1.72}
$