50=(8.5-2x)(11-2x)

Solution for 50=(8.5-2x)(11-2x) equation:

50=(8.5-2x)(11-2x)

We move all terms to the left:

50-((8.5-2x)(11-2x))=0

We add all the numbers together, and all the variables

-((-2x+8.5)(-2x+11))+50=0

We multiply parentheses ..

-((+4x^2-22x-17x+93.5))+50=0


We calculate terms in parentheses: -((+4x^2-22x-17x+93.5)), so:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-39x+93.5

Back to the equation:

-(4x^2-39x+93.5)


We get rid of parentheses

-4x^2+39x-93.5+50=0

We add all the numbers together, and all the variables

-4x^2+39x-43.5=0

a = -4; b = 39; c = -43.5;
Δ = b2-4ac
Δ = 392-4·(-4)·(-43.5)
Δ = 825
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-5\sqrt{33}}{2*-4}=\frac{-39-5\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+5\sqrt{33}}{2*-4}=\frac{-39+5\sqrt{33}}{-8}
$