(2x^2-7)^(1/2)=3-x

so FOIL the left side, square the right side for, 2x^2-7=x^2-6x+9. Add 7: 2x^2=x^2-6x+16 but then divide by 2 instead of adding 2x^2: x^2=(x^2-6x+16)(1/2).

Then subtract x^2 and get .5x^2-3x+8=0. Then use the quadratic formula to solve for x.

Is this a licit way to solve this? If not, then why not?