-9^4=-48x^2+64

Solution for -9^4=-48x^2+64 equation:

-9^4=-48x^2+64

We move all terms to the left:

-9^4-(-48x^2+64)=0

We add all the numbers together, and all the variables

-(-48x^2+64)-6561=0

We get rid of parentheses

48x^2-64-6561=0

We add all the numbers together, and all the variables

48x^2-6625=0

a = 48; b = 0; c = -6625;
Δ = b2-4ac
Δ = 02-4·48·(-6625)
Δ = 1272000
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:

$\sqrt{\Delta}=\sqrt{1272000}=\sqrt{1600*795}=\sqrt{1600}*\sqrt{795}=40\sqrt{795}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{795}}{2*48}=\frac{0-40\sqrt{795}}{96}
=-\frac{40\sqrt{795}}{96}
=-\frac{5\sqrt{795}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{795}}{2*48}=\frac{0+40\sqrt{795}}{96}
=\frac{40\sqrt{795}}{96}
=\frac{5\sqrt{795}}{12}
$