A=-2x^2+108x+111

Solution for A=-2x^2+108x+111 equation:

=-2A^2+108A+111

We move all terms to the left:

-(-2A^2+108A+111)=0

We get rid of parentheses

2A^2-108A-111=0

a = 2; b = -108; c = -111;
Δ = b2-4ac
Δ = -1082-4·2·(-111)
Δ = 12552
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:

$\sqrt{\Delta}=\sqrt{12552}=\sqrt{4*3138}=\sqrt{4}*\sqrt{3138}=2\sqrt{3138}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-2\sqrt{3138}}{2*2}=\frac{108-2\sqrt{3138}}{4}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+2\sqrt{3138}}{2*2}=\frac{108+2\sqrt{3138}}{4}
$