2(-8x^2+9)=0

Solution for 2(-8x^2+9)=0 equation:

2(-8x^2+9)=0

We multiply parentheses

-16x^2+18=0

a = -16; b = 0; c = +18;
Δ = b2-4ac
Δ = 02-4·(-16)·18
Δ = 1152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*-16}=\frac{0-24\sqrt{2}}{-32}
=-\frac{24\sqrt{2}}{-32}
=-\frac{3\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*-16}=\frac{0+24\sqrt{2}}{-32}
=\frac{24\sqrt{2}}{-32}
=\frac{3\sqrt{2}}{-4}
$