A(t)=-t(2)+6t

Solution for A(t)=-t(2)+6t equation:

(A)=-A(2)+6A

We move all terms to the left:

(A)-(-A(2)+6A)=0

We add all the numbers together, and all the variables

-(-1A^2+6A)+A=0

We get rid of parentheses

1A^2-6A+A=0

We add all the numbers together, and all the variables

A^2-5A=0

a = 1; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·1·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*1}=\frac{0}{2}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*1}=\frac{10}{2}
=5
$