X²+3x/2 + x = 11

To solve this equation, we need to simplify it first:

X² + 3x/2 + x = 11 X² + 5x/2 = 11 2X² + 5x = 22

Now, we can set the equation equal to zero:

2X² + 5x - 22 = 0

Next, we can factor the quadratic equation or use the quadratic formula to solve for X. Let's use the quadratic formula:

X = (-b ± √(b² - 4ac)) / 2a

In this case, a = 2, b = 5, and c = -22. Plugging these values into the formula:

X = (-5 ± √(5² - 4(2)(-22))) / 2(2) X = (-5 ± √(25 + 176)) / 4 X = (-5 ± √201) / 4

Therefore, the solutions for X are:

X = (-5 + √201) / 4 X = (-5 - √201) / 4

These are the two possible values for X that satisfy the original equation.