A=9x^2-8

Solution for A=9x^2-8 equation:

=9A^2-8

We move all terms to the left:

-(9A^2-8)=0

We get rid of parentheses

-9A^2+8=0

a = -9; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-9)·8
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*-9}=\frac{0-12\sqrt{2}}{-18}
=-\frac{12\sqrt{2}}{-18}
=-\frac{2\sqrt{2}}{-3}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*-9}=\frac{0+12\sqrt{2}}{-18}
=\frac{12\sqrt{2}}{-18}
=\frac{2\sqrt{2}}{-3}
$