Y=(25-2x)(15-2x)

Solution for Y=(25-2x)(15-2x) equation:

=(25-2Y)(15-2Y)

We move all terms to the left:

-((25-2Y)(15-2Y))=0

We add all the numbers together, and all the variables

-((-2Y+25)(-2Y+15))=0

We multiply parentheses ..

-((+4Y^2-30Y-50Y+375))=0


We calculate terms in parentheses: -((+4Y^2-30Y-50Y+375)), so:

(+4Y^2-30Y-50Y+375)

We get rid of parentheses

4Y^2-30Y-50Y+375

We add all the numbers together, and all the variables

4Y^2-80Y+375

Back to the equation:

-(4Y^2-80Y+375)


We get rid of parentheses

-4Y^2+80Y-375=0

a = -4; b = 80; c = -375;
Δ = b2-4ac
Δ = 802-4·(-4)·(-375)
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{-(80)-20}{2*-4}=\frac{-100}{-8}
=12+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+20}{2*-4}=\frac{-60}{-8}
=7+1/2
$