Y=(6-2n)(195-15n)

Solution for Y=(6-2n)(195-15n) equation:

=(6-2Y)(195-15Y)

We move all terms to the left:

-((6-2Y)(195-15Y))=0

We add all the numbers together, and all the variables

-((-2Y+6)(-15Y+195))=0

We multiply parentheses ..

-((+30Y^2-390Y-90Y+1170))=0


We calculate terms in parentheses: -((+30Y^2-390Y-90Y+1170)), so:

(+30Y^2-390Y-90Y+1170)

We get rid of parentheses

30Y^2-390Y-90Y+1170

We add all the numbers together, and all the variables

30Y^2-480Y+1170

Back to the equation:

-(30Y^2-480Y+1170)


We get rid of parentheses

-30Y^2+480Y-1170=0

a = -30; b = 480; c = -1170;
Δ = b2-4ac
Δ = 4802-4·(-30)·(-1170)
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(480)-300}{2*-30}=\frac{-780}{-60}
=+13
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(480)+300}{2*-30}=\frac{-180}{-60}
=+3
$