For what value of x does 25x=5x2-3?

Important:  Use " ^ " to indicate exponentiation:  25x=5x^2-3.

Rearrange these terms in descending powers of x:  5x^2 - 25x - 3 = 0

This is a quadratic equation.  To solve it, you could use a graphing calculator, the quadratic formula, completing the square or other approaches.

Let's complete the square of 5x^2 - 25x - 3 = 0:

5(x^2 - 5x)                        = 3
5(x^2 - 5x + 25/4 - 25/4)   = 3
5(x-5/2)^2    - 125/4          = 3 = 12/4
5(x-5/2)^2                         =137/4
  (x-5/2)^2     -25/4           = 137/20
  (x -5/2)^2                        = 125/20+137/20 = 162/20= 81/10
Taking the sqrt of both sides, we get:

  x-5/2                               = plus or minus 9/sqrt(10)
Then:

x = 5/2 plus or minus 9sqrt(10) / 10, or
x = 25/10 plus or minus 9sqrt(10)/10, or

       25 plus or minus 9sqrt(10)
x =
                      10