(30-2x)(21-2x)=442

Solution for (30-2x)(21-2x)=442 equation:

(30-2x)(21-2x)=442

We move all terms to the left:

(30-2x)(21-2x)-(442)=0

We add all the numbers together, and all the variables

(-2x+30)(-2x+21)-442=0

We multiply parentheses ..

(+4x^2-42x-60x+630)-442=0

We get rid of parentheses

4x^2-42x-60x+630-442=0

We add all the numbers together, and all the variables

4x^2-102x+188=0

a = 4; b = -102; c = +188;
Δ = b2-4ac
Δ = -1022-4·4·188
Δ = 7396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7396}=86$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-86}{2*4}=\frac{16}{8}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+86}{2*4}=\frac{188}{8}
=23+1/2
$