To solve the equation 5x² + 4x – 9 = 0, we can use the quadratic formula, which is:
x = (-b ± √(b² – 4ac)) / 2a
In our case, a = 5, b = 4, and c = -9. Let’s plug these values into the formula.
First, we need to calculate the discriminant, which is b² – 4ac:
= 4² – 4(5)(-9) = 16 + 180 = 196
Now that we have the discriminant, we can substitute it into the quadratic formula:
x = (-4 ± √196) / (2 * 5)
Calculating the square root of 196 gives us 14:
x = (-4 ± 14) / 10
This results in two possible solutions:
x = (10) / 10 = 1
x = (-18) / 10 = -1.8
Thus, the solutions to the equation 5x² + 4x – 9 = 0 are:
x = 1 and x = -1.8