First you must rewrite the given equation in standard form:
2x^2 - 4x + 7 = 0. Here a=2, b=-4 and c=7.
The solutions are thus
-[-4] plus or minus sqrt( [-4]^2 - 4[2][7] )
x = --------------------------------------------------------
4
4 plus or minus sqrt (16 - 56)
or: x = --------------------------------------------
4
16-56 = - 40, a negative number. Thus, we must introduce the imaginary operator: sqrt (-40) = 2i*sqrt(10)
The roots are thus:
4 plus or minus 2i sqrt(10) 2 plus or minus i*sqrt(10)
x = ----------------------------------------- = ---------------------------------------
4 2