18-8x^2=-54

Solution for 18-8x^2=-54 equation:

18-8x^2=-54

We move all terms to the left:

18-8x^2-(-54)=0

We add all the numbers together, and all the variables

-8x^2+72=0

a = -8; b = 0; c = +72;
Δ = b2-4ac
Δ = 02-4·(-8)·72
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48}{2*-8}=\frac{-48}{-16}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*-8}=\frac{48}{-16}
=-3
$