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# exact solution help

Find the exact solution simplify as much as possible and show work

5x2+1=4x

### 1 Answer by Expert Tutors

Philip P. | Effective and Affordable Math TutorEffective and Affordable Math Tutor
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5x2 + 1 = 4x

First, put the equation into standard form:

5x2 - 4x + 1 = 0

This equation's roots are complex numbers; it has no roots in the set of real numbers.  To show this, compute the coordinates of the parabola's vertex.  The x-coordinate is located at x = -b/2a (where a=5 and b=-4).  To find the y-coordinate, plug the value of the x coordinate of the vertex into your quadratic equation.

Since the coefficient of the x2 term is positive (5), the parabola opens upward.  If the y-coordinate of the vertex is positive, then the parabola will not cross the x-axis and will have no real roots.  (The roots are the points where the graph crosses the x-axis)

To find the complex roots, use the quadratic formula:

x = (-b/2a) ± (1/2a)√(b2-4ac)

For this problem, a = 5, b = -4, c = 1.  Plug those values into the quadratic formula to get the answer.