this is equivalent to:
2 * (x^4) ^ 2 - 7 * (x^4) ^ 1 - 3 = 0
if you replace x^4 with y, the equation becomes:
2y^2 - 7y - 3 = 0
this in standard form of ax^2 + bx + c = 0
when you replace x with y, it becomes:
ay^2 + by + c = 0
if you solve the quadratic equation using the quadratic formula, you will get:
y = 3.886000936 or y = -0.386000936
since y = x^4, solve this for x to get:
x = (3.886000936) ^ (1/4) or y = (-0.386000936) ^ (1/4).
you will find that the first option will get you x = plus or minus 1.404027859.
you will find that the second option will get you x = undefined because you can't take the even root of a negative number and get a real number as an answer.
you can get a complex number as an answer, but not a real number.
your solution becomes:
x = plus or minus fourth root of 3.886000936 which is equal to plus or minus 1.404027859.
if you graph the equation of y = 2x^8 - 7x^4 - 3, you will find that the roots are plus or minus 1.404 when rounded to 3 decimal places, as shown below.
here is the quadratic formula.
(-b plus or minus sqrt(b^2 - 4ac)
x = --------------------------------------
2a