(8.5-2x)(11-2x)=0

Solution for (8.5-2x)(11-2x)=0 equation:

(8.5-2x)(11-2x)=0

We add all the numbers together, and all the variables

(-2x+8.5)(-2x+11)=0

We multiply parentheses ..

(+4x^2-22x-17x+93.5)=0

We get rid of parentheses

4x^2-22x-17x+93.5=0

We add all the numbers together, and all the variables

4x^2-39x+93.5=0

a = 4; b = -39; c = +93.5;
Δ = b2-4ac
Δ = -392-4·4·93.5
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-5}{2*4}=\frac{34}{8}
=4+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+5}{2*4}=\frac{44}{8}
=5+1/2
$