Y=0.05(x-30)(x-70)

Solution for Y=0.05(x-30)(x-70) equation:

=0.05(Y-30)(Y-70)

We move all terms to the left:

-(0.05(Y-30)(Y-70))=0

We multiply parentheses ..

-(0.05(+Y^2-70Y-30Y+2100))=0


We calculate terms in parentheses: -(0.05(+Y^2-70Y-30Y+2100)), so:

0.05(+Y^2-70Y-30Y+2100)

We multiply parentheses

0.05Y^2-3.5Y-1.5Y+105

We add all the numbers together, and all the variables

0.05Y^2-5Y+105

Back to the equation:

-(0.05Y^2-5Y+105)


We get rid of parentheses

-0.05Y^2+5Y-105=0

a = -0.05; b = 5; c = -105;
Δ = b2-4ac
Δ = 52-4·(-0.05)·(-105)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-2}{2*-0.05}=\frac{-7}{-0.1}
=+70
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+2}{2*-0.05}=\frac{-3}{-0.1}
=+30
$