P(t)=-2(t+3)(t+5)

Solution for P(t)=-2(t+3)(t+5) equation:

(P)=-2(P+3)(P+5)

We move all terms to the left:

(P)-(-2(P+3)(P+5))=0

We multiply parentheses ..

-(-2(+P^2+5P+3P+15))+P=0


We calculate terms in parentheses: -(-2(+P^2+5P+3P+15)), so:

-2(+P^2+5P+3P+15)

We multiply parentheses

-2P^2-10P-6P-30

We add all the numbers together, and all the variables

-2P^2-16P-30

Back to the equation:

-(-2P^2-16P-30)


We get rid of parentheses

2P^2+16P+P+30=0

We add all the numbers together, and all the variables

2P^2+17P+30=0

a = 2; b = 17; c = +30;
Δ = b2-4ac
Δ = 172-4·2·30
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-7}{2*2}=\frac{-24}{4}
=-6
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+7}{2*2}=\frac{-10}{4}
=-2+1/2
$