First, add #color(red)(5)# to each side of the equation to isolate the #x# term while keeping the equation balanced:

#2x^2 - 5 + color(red)(5) = 93 + color(red)(5)#

#2x^2 - 0 = 98#

#2x^2 = 98#

Now, divide each side of the equation by #color(red)(2)# to isolate the #x^2# while keeping the equation balanced:

#(2x^2)/color(red)(2) = 98/color(red)(2)#

#(color(red)(cancel(color(black)(2)))x^2)/cancel(color(red)(2)) = 49#

#x^2 = 49#

Now, take the square root of each side of the equation to solve for #x#. Remember, the square root of a number produces a positive and negative result:

#sqrt(x^2) = +-sqrt(49)#

#x = +-7#

#x = {-7, 7}#