3x-5+7x=3x^2+7+11x

To solve the given equation, we can start by simplifying both sides.

3x - 5 + 7x = 3x^2 + 7 + 11x

Combine like terms on the left side:

3x + 7x - 5 = 3x^2 + 11x + 7

10x - 5 = 3x^2 + 11x + 7

Next, move all terms to one side of the equation to set it equal to zero:

3x^2 + 11x + 7 - 10x + 5 = 0

3x^2 + x + 12 = 0

Now, the equation is in the standard form of a quadratic equation (ax^2 + bx + c = 0). To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2-4ac)) / 2a

In this case, a = 3, b = 1, and c = 12. Substituting these values into the formula:

x = (-1 ± √(1^2 - 4312)) / (2*3)

x = (-1 ± √(1 - 144)) / 6

x = (-1 ± √(-143)) / 6

Since the square root of -143 is an imaginary number, the solutions will be complex numbers:

x = (-1 ± √143i) / 6

Therefore, the solutions to the given equation are:

x = (-1 + √143i) / 6 and x = (-1 - √143i) / 6