(21-2x)(27-2x)=391

Solution for (21-2x)(27-2x)=391 equation:

(21-2x)(27-2x)=391

We move all terms to the left:

(21-2x)(27-2x)-(391)=0

We add all the numbers together, and all the variables

(-2x+21)(-2x+27)-391=0

We multiply parentheses ..

(+4x^2-54x-42x+567)-391=0

We get rid of parentheses

4x^2-54x-42x+567-391=0

We add all the numbers together, and all the variables

4x^2-96x+176=0

a = 4; b = -96; c = +176;
Δ = b2-4ac
Δ = -962-4·4·176
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-80}{2*4}=\frac{16}{8}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+80}{2*4}=\frac{176}{8}
=22
$