Y=(30t-5t^2)

Solution for Y=(30t-5t^2) equation:

=(30Y-5Y^2)

We move all terms to the left:

-((30Y-5Y^2))=0


We calculate terms in parentheses: -((30Y-5Y^2)), so:

(30Y-5Y^2)

We get rid of parentheses

-5Y^2+30Y

Back to the equation:

-(-5Y^2+30Y)


We get rid of parentheses

5Y^2-30Y=0

a = 5; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·5·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*5}=\frac{0}{10}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*5}=\frac{60}{10}
=6
$