The object is to get x by itself and then "switch" x and y......we can write
y = 2x^2 - 3 add 3 to both sides
y + 3 = 2x^2 divide both sides by 2
[ y + 3 ] / 2 = x^2 take both roots
±√ [ (y + 3) / 2 ] = x "switch" x and y
±√ [ ( x + 3) / 2 ] = y = the inverse