Answer: the solutions to the equation are x = √(10/3) and x = -√(10/3).
Explanation:
To solve the equation 10 - 9x^2 + 4x = -6x^2 + 4x, we can simplify it and then solve for x.
Rearranging the equation, we have:
10 - 9x^2 + 4x = -6x^2 + 4x
Combining like terms, we get:
10 - 9x^2 = -6x^2
Subtracting -6x^2 from both sides, we have:
10 - 9x^2 + 6x^2 = 0
Simplifying further, we get:
10 - 3x^2 = 0
To solve for x, we can isolate the term with x^2:
-3x^2 = -10
Dividing both sides by -3, we have:
x^2 = 10/3
Taking the square root of both sides, we get:
x = ±√(10/3)
Therefore, the solutions to the equation are x = √(10/3) and x = -√(10/3).