Let y=x-{(a+b)/2}

then the given equation reduces to

16y^{4}+24y^{2}(a-b)^{2}-7(a-b)^{4}=0

which on solving gives

y=+-i\sqrt{7}(a-b)/2 or, y=+-(a-b)/2

which gives two complex roots and two real roots.