Strong shaking

sounds like a bad motor mount. give those a quick check.

Yeah it wouldnt be the brakes then, i want to say its something suspension related, but it cant be if it does the same thing at idle. other than the motor mounts you, it could maybe be a dirty MAF sensor, that could cause the car to shake i suppose. But i would lean towards a broken passenger side motor mount

Inner/Outer Tie-Rod on passenger side. To check.. carefully jack the front end off the ground so the tire does not touch and can spin freely. Now, kneeling directly center in front of the wheel, grab the very center of the left and right side of the tire and act like you are trying to pull it off by wiggling in and out... like you are trying to steer the wheel. It should be tight, with NO play at all (not loose). If it makes a knocking noise and moves too easy, the inner or outer tie rod is bad.

Also, while the car is still lifted, grab the top and bottom of the wheel this time instead of the sides..and do the same thing. This checks for a bad/worn ball joint. Sometimes it won't move easily by hand and it will seem like it is good. But still check it anyway.

Remember to make sure the car is properly secure before performing this. You will be trying to move something on the car and you don't want it falling and hurting you.