A(x)=-8x2+6

Solution for A(x)=-8x2+6 equation:

(A)=-8A^2+6

We move all terms to the left:

(A)-(-8A^2+6)=0

We get rid of parentheses

8A^2+A-6=0

a = 8; b = 1; c = -6;
Δ = b2-4ac
Δ = 12-4·8·(-6)
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{193}}{2*8}=\frac{-1-\sqrt{193}}{16}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{193}}{2*8}=\frac{-1+\sqrt{193}}{16}
$