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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-1x+(-2x+11)(-2x+8.5)=0

We multiply parentheses ..

(+4x^2-17x-22x+93.5)-1x=0

We get rid of parentheses

4x^2-17x-22x-1x+93.5=0

We add all the numbers together, and all the variables

4x^2-40x+93.5=0

a = 4; b = -40; c = +93.5;
Δ = b2-4ac
Δ = -402-4·4·93.5
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{26}}{2*4}=\frac{40-2\sqrt{26}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{26}}{2*4}=\frac{40+2\sqrt{26}}{8}
$