A=-3x^2+82x+23

Solution for A=-3x^2+82x+23 equation:

=-3A^2+82A+23

We move all terms to the left:

-(-3A^2+82A+23)=0

We get rid of parentheses

3A^2-82A-23=0

a = 3; b = -82; c = -23;
Δ = b2-4ac
Δ = -822-4·3·(-23)
Δ = 7000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7000}=\sqrt{100*70}=\sqrt{100}*\sqrt{70}=10\sqrt{70}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-10\sqrt{70}}{2*3}=\frac{82-10\sqrt{70}}{6}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+10\sqrt{70}}{2*3}=\frac{82+10\sqrt{70}}{6}
$