A=-2x^2+24x-3

Solution for A=-2x^2+24x-3 equation:

=-2A^2+24A-3

We move all terms to the left:

-(-2A^2+24A-3)=0

We get rid of parentheses

2A^2-24A+3=0

a = 2; b = -24; c = +3;
Δ = b2-4ac
Δ = -242-4·2·3
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{138}}{2*2}=\frac{24-2\sqrt{138}}{4}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{138}}{2*2}=\frac{24+2\sqrt{138}}{4}
$