Find the roots of 2x^2-2x=3, leaving your answer in it's simplest exact form.

First we need to rearrange our equation so it is in the correct form of ax²+bx+c=0.So we'd move the 3 over to the left hand side to give us 2x2-2x-3=0.We need to use the quadratic formula. Using x=( -b+/-(b²-4ac)^1/2)/2a, where a=2, b=-2, c=-3.This gives us the roots x=(2+/-(28)^1/2)/4 which is correct but is not in its simplist form. Use surd rules to simplify the 28^1/2 .Final answer of 1/2 +/- 1/2(7)^1/2.