Respuesta :

Medunno13

Answer: [tex]-1, \frac{4}{3}[/tex]

Step-by-step explanation:

[tex]3x^{2}-5x+6=10-4x\\\\3x^{2}-x-4=0\\ \\ (x+1)(3x-4)=0 \\ \\ x=\boxed{-1, \frac{4}{3}}[/tex]

chetankachana

Answer:

x = -1
x = 4/3

Step-by-step explanation:

Hello!

First, let's convert the equation into Standard Form: [tex]ax^2 + bx + c = 0[/tex]

  • [tex]3x^2 - 5x + 6 = 10 - 4x[/tex]
  • [tex]3x^2 - x - 4 = 0[/tex]

We can solve this by factoring the quadratic. We have to find two numbers that multiply to [tex]ac[/tex] but add up to [tex]b[/tex].

  • ac = -12
  • b = -1

The two numbers would be -4 and 3. We can expand -x to -4x + 3x, and then factor by grouping.

Factor

  • [tex]3x^2 - x - 4 = 0[/tex]
  • [tex]3x^2 +3x - 4x - 4 = 0[/tex]
  • [tex]3x(x + 1) - 4(x + 1) = 0[/tex]
  • [tex](3x - 4)(x + 1) = 0[/tex]

Use the Zero Product Property. Set each factor to zero and solve for x.

3x - 4 = 0

  • 3x = 4
  • x = 4/3

x + 1 = 0

  • x = -1

The solutions to the quadratic are -1 and 4/3.

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