How do I solve the equation 5x^2=8x+2 using the quadratic formula?

To solve an equation means to determine it's roots. Since
it is a quadratic equation, it will have 2 roots.

The
quadratic formula is used to determine the roots:

x1 =
[-b+sqrt(delta)]/2a and x2 =
[-b-sqrt(delta)]/2a

discriminant = delta = b^2 -
4ac

We'll identify the coefficient of the quadratic:
a,b,c.

a = 5, b = -8 and c =
-2

delta = (-8)^2 -
4*5*(-2)

delta = 64 + 40

delta
= 104

We'll take square root both
sides:

sqrt delta = sqrt
104

sqrt delta = 2sqrt 26

x1 =
(8 + 2sqrt 26)/2*5

x1 = (4 +
sqrt26)/5

x2 = (4 -
sqrt26)/5

The roots of the quadratic are: x1
= (4 + sqrt26)/5 and x2 = (4 - sqrt26)/5.