A(t)=10t-5t^2

Solution for A(t)=10t-5t^2 equation:

(A)=10A-5A^2

We move all terms to the left:

(A)-(10A-5A^2)=0

We get rid of parentheses

5A^2-10A+A=0

We add all the numbers together, and all the variables

5A^2-9A=0

a = 5; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·5·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*5}=\frac{0}{10}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*5}=\frac{18}{10}
=1+4/5
$