To solve the quadratic equation 5x^2 + 8x - 4 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 5, b = 8, and c = -4. Plugging these values into the formula, we get:

x = (-8 ± √(8^2 - 45(-4))) / 2*5
x = (-8 ± √(64 + 80)) / 10
x = (-8 ± √144) / 10
x = (-8 ± 12) / 10

Now we have two possible solutions for x:

x₁ = (-8 + 12) / 10
x₁ = 4 / 10
x₁ = 0.4

x₂ = (-8 - 12) / 10
x₂ = -20 / 10
x₂ = -2

Therefore, the solutions to the quadratic equation 5x^2 + 8x - 4 = 0 are x = 0.4 and x = -2.