(8-2x)(11-2x)=54

Solution for (8-2x)(11-2x)=54 equation:

(8-2x)(11-2x)=54

We move all terms to the left:

(8-2x)(11-2x)-(54)=0

We add all the numbers together, and all the variables

(-2x+8)(-2x+11)-54=0

We multiply parentheses ..

(+4x^2-22x-16x+88)-54=0

We get rid of parentheses

4x^2-22x-16x+88-54=0

We add all the numbers together, and all the variables

4x^2-38x+34=0

a = 4; b = -38; c = +34;
Δ = b2-4ac
Δ = -382-4·4·34
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-30}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+30}{2*4}=\frac{68}{8}
=8+1/2
$