A=-4x^2+38x+99

Solution for A=-4x^2+38x+99 equation:

=-4A^2+38A+99

We move all terms to the left:

-(-4A^2+38A+99)=0

We get rid of parentheses

4A^2-38A-99=0

a = 4; b = -38; c = -99;
Δ = b2-4ac
Δ = -382-4·4·(-99)
Δ = 3028
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:

$\sqrt{\Delta}=\sqrt{3028}=\sqrt{4*757}=\sqrt{4}*\sqrt{757}=2\sqrt{757}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{757}}{2*4}=\frac{38-2\sqrt{757}}{8}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{757}}{2*4}=\frac{38+2\sqrt{757}}{8}
$