To find the solutions of the equation 4x² – 7x + 3 = 24, we first need to set the equation to zero. This is done by subtracting 24 from both sides:
4x² – 7x + 3 – 24 = 0
This simplifies to:
4x² – 7x – 21 = 0
Next, we can use the quadratic formula to find the values of x. The quadratic formula is:
x = (-b ± √(b² – 4ac)) / 2a
In our equation, a = 4, b = -7, and c = -21. Now, we will calculate the discriminant:
b² – 4ac = (-7)² – 4(4)(-21)
49 + 336 = 385
Now we can plug the values into the quadratic formula:
x = (7 ± √385) / 8
This gives us two solutions:
x₁ = (7 + √385) / 8
x₂ = (7 – √385) / 8
So, the solutions to the equation 4x² – 7x – 21 = 0 are:
- x₁ ≈ 3.80
- x₂ ≈ -2.21