A(0)=-2w^2+300w

Solution for A(0)=-2w^2+300w equation:

(0)=-2A^2+300A

We move all terms to the left:

(0)-(-2A^2+300A)=0

We add all the numbers together, and all the variables

-(-2A^2+300A)=0

We get rid of parentheses

2A^2-300A=0

a = 2; b = -300; c = 0;
Δ = b2-4ac
Δ = -3002-4·2·0
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-300}{2*2}=\frac{0}{4}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+300}{2*2}=\frac{600}{4}
=150
$