Question

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

Answer 1

2x²+6x-3x-9-2x+x²=0
3x²+x-9=0
D=b²-4ac
D=1+108
D=109
x=-b-+√D:2a
x1=-1-√109:6
x2=-1+√109:6

Answer 2

Let's simplify the given expression and solve for x:

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

Expanding the brackets, we have:

(2x^2 + 6x - 3x - 9) - (2x - x^2) = 0

Combining like terms, we get:

2x^2 + 6x - 3x - 9 - 2x + x^2 = 0

Rearranging the terms, we have:

2x^2 + x^2 + 6x - 3x - 2x - 9 = 0

Combining like terms again, we get:

3x^2 + x - 9 = 0

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this equation, a = 3, b = 1, and c = -9. Substituting these values, we get:

x = (-(1) ± √((1)^2 - 4(3)(-9))) / (2(3))

Simplifying further:

x = (-1 ± √(1 + 108)) / 6

x = (-1 ± √109) / 6

Therefore, the solutions to the equation (2x - 3)(x + 3) - x(2 - x) = 0 are:

x = (-1 + √109) / 6 x = (-1 - √109) / 6