(18-2x)(11-2x)=1

Solution for (18-2x)(11-2x)=1 equation:

(18-2x)(11-2x)=1

We move all terms to the left:

(18-2x)(11-2x)-(1)=0

We add all the numbers together, and all the variables

(-2x+18)(-2x+11)-1=0

We multiply parentheses ..

(+4x^2-22x-36x+198)-1=0

We get rid of parentheses

4x^2-22x-36x+198-1=0

We add all the numbers together, and all the variables

4x^2-58x+197=0

a = 4; b = -58; c = +197;
Δ = b2-4ac
Δ = -582-4·4·197
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-2\sqrt{53}}{2*4}=\frac{58-2\sqrt{53}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+2\sqrt{53}}{2*4}=\frac{58+2\sqrt{53}}{8}
$