Algebra Examples

$3 x^{2} - x - 4 = 0$

Step 1

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 2

Substitute the values $a = 3$ , $b = - 1$ , and $c = - 4$ into the quadratic formula and solve for $x$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (3 \cdot - 4)}}{2 \cdot 3}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise $- 1$ to the power of $2$ .

$x = \frac{1 \pm \sqrt{1 - 4 \cdot 3 \cdot - 4}}{2 \cdot 3}$

Step 3.1.2

Multiply $- 4 \cdot 3 \cdot - 4$ .

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Step 3.1.2.1

Multiply $- 4$ by $3$ .

$x = \frac{1 \pm \sqrt{1 - 12 \cdot - 4}}{2 \cdot 3}$

Step 3.1.2.2

Multiply $- 12$ by $- 4$ .

$x = \frac{1 \pm \sqrt{1 + 48}}{2 \cdot 3}$

Step 3.1.3

Add $1$ and $48$ .

$x = \frac{1 \pm \sqrt{49}}{2 \cdot 3}$

Step 3.1.4

Rewrite $49$ as $7^{2}$ .

$x = \frac{1 \pm \sqrt{7^{2}}}{2 \cdot 3}$

Step 3.1.5

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{1 \pm 7}{2 \cdot 3}$

Step 3.2

Multiply $2$ by $3$ .

$x = \frac{1 \pm 7}{6}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{4}{3}, - 1$