# 4x ^ 2 – 5x – 12 = 0

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.

1. First, plug these values into the quadratic formula:

X = (-(-5) ± √((-5)² – 4(4)(-12))) / (2(4))

1. Simplify the equation:

X = (5 ± √(25 + 192)) / 8

1. Calculate the values under the square root:

X = (5 ± √217) / 8

1. 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

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