A=-x2+27x-162

Solution for A=-x2+27x-162 equation:

=-A2+27A-162

We move all terms to the left:

-(-A2+27A-162)=0

We add all the numbers together, and all the variables

-(-1A^2+27A-162)=0

We get rid of parentheses

1A^2-27A+162=0

We add all the numbers together, and all the variables

A^2-27A+162=0

a = 1; b = -27; c = +162;
Δ = b2-4ac
Δ = -272-4·1·162
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{-(-27)-9}{2*1}=\frac{18}{2}
=9
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+9}{2*1}=\frac{36}{2}
=18
$