First, add #color(red)(18)# to each side of the equation to isolate the #x# term while keeping the equation balanced:
#32x^2 - 18 + color(red)(18) = 0 + color(red)(18)#
#32x^2 - 0 = 18#
#32x^2 = 18#
Next, divide each side of the equation by #color(red)(32)# to isolate the #x^2# term while keeping the equation balanced:
#(32x^2)/color(red)(32) = 18/color(red)(32)#
#(color(red)(cancel(color(black)(32)))x^2)/cancel(color(red)(32)) = (2 xx 9)/color(red)(2 xx 16)#
#x^2 = (color(red)(cancel(color(black)(2))) xx 9)/color(red)(color(black)(cancel(color(red)(2))) xx 16)#
#x^2 = 9/16#
Now, take the square root of each side of the equation to solve for #x# while keeping the equation balanced. Remember, taking the square root of a number produces a negative and positive result:
#sqrt(x^2) = sqrt(9/16)#
#x = sqrt(9)/sqrt(16)#
#x = +-3/4#