Question

3x^2 + 13x = 2x^2 - x -49 x^2 - 2\3x = 8\3

Answer 1

$3 x^{2} -2x-8=0$
$D=4+4*3*8=100$
$x_{1} = \frac{2+10}{6} =2$
$x_{2} = \frac{2-10}{6} =- \frac{8}{6}=- \frac{4}{3}=-1 \frac{1}{3}$

Answer 2

To solve the equations:

1. 3x^2 + 13x = 2x^2 - x - 49 First, let's simplify the equation by combining like terms: 3x^2 + 13x - 2x^2 + x + 49 = 0 x^2 + 14x + 49 = 0

The equation is now in the form of a quadratic equation (ax^2 + bx + c = 0), where a = 1, b = 14, and c = 49. We can solve this quadratic equation by factoring or by using the quadratic formula. Let's use factoring:

(x + 7)(x + 7) = 0 (x + 7)^2 = 0

Now, set each factor equal to zero: x + 7 = 0

Solving for x: x = -7

Therefore, the solution to the equation 3x^2 + 13x = 2x^2 - x - 49 is x = -7.

2. x^2 - (2/3)x = (8/3) To solve this equation, let's first clear the fractions by multiplying every term by 3: 3(x^2) - 2x = 8

Now, let's rearrange the equation to the standard quadratic form: 3x^2 - 2x - 8 = 0

We can solve this quadratic equation using factoring or the quadratic formula. Let's use factoring:

(3x + 4)(x - 2) = 0

Now, set each factor equal to zero: 3x + 4 = 0 or x - 2 = 0

Solving for x: 3x = -4 x = -4/3

x = 2

Therefore, the solutions to the equation x^2 - (2/3)x = (8/3) are x = -4/3 and x = 2.