Question

Solve for x
3x² - 5x + 6 = 10 - 4x​

Answer 1

Answer:
`-1, (4)/(3)`

Explanation:

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

Answer 2

x = -1
x = 4/3

Explanation:

Hello!

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

• 
  `3x^2 - 5x + 6 = 10 - 4x`
• 
  `3x^2 - x - 4 = 0`

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

• 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

• 
  `3x^2 - x - 4 = 0`
• 
  `3x^2 +3x - 4x - 4 = 0`
• 
  `3x(x + 1) - 4(x + 1) = 0`
• 
  `(3x - 4)(x + 1) = 0`

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.