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Another way to do this is to place the original problem in the form:  ax² + bx + c  =  0

and then find the value of the discriminant:  b² - 4ac  (the portion under the square root sign in the quadratic formula).

If this value is zero, there will be one answer; if this value is positive, there will be two (unequal) real answers; if this value is negative there will be two (unequal) imaginary answers.

5  =  17x² - 200x     --->     subtract 5 from both sides and exchange the sides    --->     17x² - 200x - 5  =  0

So,  a = 17,   b = -200,  and  c = -5

b² - 4ac  =  (-200)² - 4(17)(-5)  =  40340

Since this value is positive, there will be two, unequal, real answer.

Solve for x:
17 x^2-200 x = 5

Divide both sides by 17:
x^2-(200 x)/17 = 5/17

Add 10000/289 to both sides:
x^2-(200 x)/17+10000/289 = 10085/289

Write the left hand side as a square:
(x-100/17)^2 = 10085/289

Take the square root of both sides:
x-100/17 = sqrt(10085)/17 or x-100/17 = -sqrt(10085)/17

Add 100/17 to both sides:
x = 100/17+sqrt(10085)/17 or x-100/17 = -sqrt(10085)/17

Add 100/17 to both sides:
Answer: | x = 100/17+sqrt(10085)/17      or       x = 100/17-sqrt(10085)/17

 

Now, you can see the answer for yourself.