(7-2x)(11-2x)=192

Solution for (7-2x)(11-2x)=192 equation:

(7-2x)(11-2x)=192

We move all terms to the left:

(7-2x)(11-2x)-(192)=0

We add all the numbers together, and all the variables

(-2x+7)(-2x+11)-192=0

We multiply parentheses ..

(+4x^2-22x-14x+77)-192=0

We get rid of parentheses

4x^2-22x-14x+77-192=0

We add all the numbers together, and all the variables

4x^2-36x-115=0

a = 4; b = -36; c = -115;
Δ = b2-4ac
Δ = -362-4·4·(-115)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-56}{2*4}=\frac{-20}{8}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+56}{2*4}=\frac{92}{8}
=11+1/2
$