Y=(20-2x)(30-2x)

Solution for Y=(20-2x)(30-2x) equation:

=(20-2Y)(30-2Y)

We move all terms to the left:

-((20-2Y)(30-2Y))=0

We add all the numbers together, and all the variables

-((-2Y+20)(-2Y+30))=0

We multiply parentheses ..

-((+4Y^2-60Y-40Y+600))=0


We calculate terms in parentheses: -((+4Y^2-60Y-40Y+600)), so:

(+4Y^2-60Y-40Y+600)

We get rid of parentheses

4Y^2-60Y-40Y+600

We add all the numbers together, and all the variables

4Y^2-100Y+600

Back to the equation:

-(4Y^2-100Y+600)


We get rid of parentheses

-4Y^2+100Y-600=0

a = -4; b = 100; c = -600;
Δ = b2-4ac
Δ = 1002-4·(-4)·(-600)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20}{2*-4}=\frac{-120}{-8}
=+15
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20}{2*-4}=\frac{-80}{-8}
=+10
$