Solve using the quadratic formula of 4 { x }^{2} - 5 x - 12 = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

5^{2} + 192

Evaluate the power

25 + 192

Add the numbers

217

x = \frac{5 \pm 217}{8}

Separate the equation into 2 possible cases

x = \frac{5 + 217}{8} x = \frac{5 - 217}{8}

Solution

x_{1} = \frac{5 - 217}{8}, x_{2} = \frac{5 + 217}{8}

Alternative Form

x_{1} \approx - 1.216365, x_{2} \approx 2.466365

Show Solution

Graph

Frequently Asked Questions

Solve using the quadratic formula of $4 { x }^{2} - 5 x - 12 = 0$

$x_{1} = \frac{5 - 217}{8}, x_{2} = \frac{5 + 217}{8}$
Solve by completing the square of $4 { x }^{2} - 5 x - 12 = 0$

$x_{1} = \frac{- 217 + 5}{8}, x_{2} = \frac{217 + 5}{8}$
Solve using the PQ formula of $4 { x }^{2} - 5 x - 12 = 0$

$x_{1} = \frac{5 - 217}{8}, x_{2} = \frac{5 + 217}{8}$

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English

4 x ^2 - 5 x - 12 = 0

Solve the quadratic equation

Graph

Frequently Asked Questions

Solve using the quadratic formula of \(4 { x }^{2} - 5 x - 12 = 0\)

Solve by completing the square of \(4 { x }^{2} - 5 x - 12 = 0\)

Solve using the PQ formula of \(4 { x }^{2} - 5 x - 12 = 0\)