To solve the given equation:
3x(x + 5) = 5x(12 - x) - 5
First, let's simplify both sides of the equation step by step:
Distribute on both sides:
- 3x^2 + 15x = 60x - 5x^2 - 5
Combine like terms on the right side:
Move all terms to one side of the equation:
Simplify:
Now, you have a quadratic equation in standard form. To solve for x, you can use the quadratic formula:
- x = (-b ± √(b^2 - 4ac)) / 2a
In this case, the coefficients are:
Plug these values into the quadratic formula:
- x = (-(-40) ± √((-40)^2 - 4 * 3 * 5)) / (2 * 3)
- x = (40 ± √(1600 - 60)) / 6
- x = (40 ± √(1540)) / 6
- x = (40 ± √(4 * 385)) / 6
- x = (40 ± 2√385) / 6
So, the solutions for the equation are:
- x = (40 + 2√385) / 6
- x = (40 - 2√385) / 6
These are the values of x that satisfy the given equation.