How do you find the discriminant for #x^2-4/5x=3# and determine the number and type of solutions?

1 Answer
Nov 21, 2017

Answer:

See a solution process below:

Explanation:

First, rewrite the equation in standard form as:

#x^2 - 4/5x - 3 = 0#

The quadratic formula states:

For #ax^2 + bx + c = 0#, the values of #x# which are the solutions to the equation are given by:

#x = (-b +- sqrt(b^2 - 4ac))/(2a)#

The discriminate is the portion of the quadratic equation within the radical: #color(blue)(b)^2 - 4color(red)(a)color(green)(c)#

If the discriminate is:
- Positive, you will get two real solutions
- Zero you get just ONE solution
- Negative you get complex solutions

To find the discriminant for this problem substitute:

#color(red)(1)# for #color(red)(a)#

#color(blue)(-4/5)# for #color(blue)(b)#

#color(green)(3)# for #color(green)(c)#

#color(blue)(-3)^2 - (4 * color(red)(1) * color(green)(-4/5))#

#9 - (-16/5)#

#9 + 16/5#

#9 + 15/5 + 1/5#

#9 + 3 + 1/5#

#12 + 1/5#

#12 1/5# or #61/5#

Because the discriminate is positive there will two (2) real solutions for this equation.