(10-2x)(11-2x)=54

Solution for (10-2x)(11-2x)=54 equation:

(10-2x)(11-2x)=54

We move all terms to the left:

(10-2x)(11-2x)-(54)=0

We add all the numbers together, and all the variables

(-2x+10)(-2x+11)-54=0

We multiply parentheses ..

(+4x^2-22x-20x+110)-54=0

We get rid of parentheses

4x^2-22x-20x+110-54=0

We add all the numbers together, and all the variables

4x^2-42x+56=0

a = 4; b = -42; c = +56;
Δ = b2-4ac
Δ = -422-4·4·56
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{217}}{2*4}=\frac{42-2\sqrt{217}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{217}}{2*4}=\frac{42+2\sqrt{217}}{8}
$