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

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Answer 1 · 2017-11-21T23:35:59

See a solution process below:

First, rewrite the equation in standard form as:

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

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.

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