To solve the quadratic equation 4X^2 – 5X – 12 = 0, you can use the quadratic formula:
X = (-B ± √(B² – 4AC)) / (2A)
In this equation, A = 4, B = -5, and C = -12.
- First, plug these values into the quadratic formula:
X = (-(-5) ± √((-5)² – 4(4)(-12))) / (2(4))
- Simplify the equation:
X = (5 ± √(25 + 192)) / 8
- Calculate the values under the square root:
X = (5 ± √217) / 8
- Now, you have two solutions, one with a plus sign and one with a minus sign:
X₁ = (5 + √217) / 8 = 2.696
X₂ = (5 – √217) / 8 = -1.696
So, the solutions to the quadratic equation 4X^2 – 5X – 12 = 0 are:
X₁ ≈ 2.696
X₂ ≈ -1.696