A(x)=-2x2+36x

Solution for A(x)=-2x2+36x equation:

(A)=-2A^2+36A

We move all terms to the left:

(A)-(-2A^2+36A)=0

We get rid of parentheses

2A^2-36A+A=0

We add all the numbers together, and all the variables

2A^2-35A=0

a = 2; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·2·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*2}=\frac{0}{4}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*2}=\frac{70}{4}
=17+1/2
$