Question

(х+4)(2х-3)-(5х-6)(х-3)=10 дискриминант

Answer 1

$2 {x}^{2} - 3x + 8x - 12 -5 {x}^{2} - 15x - 6x + 18 = 10 \\ 7 {x}^{2} - 16x + 4 = 0 \\ d = 256 - 4 \times 7 \times 4 = 256 - 112 = 144 = {12}^{2} \\ x1 = \frac{16 + 12}{14} = \frac{28}{14} = 2 \\ x2 = \frac{16 - 12}{14} = \frac{4}{14} = \frac{2}{7}$

Answer 2

To solve this equation and find the discriminant, let's first simplify the left-hand side of the equation:

(х+4)(2х-3) - (5х-6)(х-3) = 10

Expand the products:

2х^2 + 8х - 3х - 12 - (5х^2 - 15х - 6х + 18) = 10

Combine like terms:

2х^2 + 8х - 3х - 12 - 5х^2 + 15х + 6х - 18 = 10

Simplify:

-3х^2 + 6х - 12 = 10

Now, move everything to one side of the equation:

-3х^2 + 6х - 12 - 10 = 0

Simplify further:

-3х^2 + 6х - 22 = 0

Now we have a quadratic equation in the form of ax^2 + bx + c = 0, where a = -3, b = 6, and c = -22. To find the discriminant (Δ), which is used to determine the nature of the solutions of a quadratic equation, you can use the formula:

Δ = b^2 - 4ac

Plugging in the values:

Δ = (6)^2 - 4(-3)(-22) Δ = 36 - 264 Δ = -228

The discriminant (Δ) is -228.