Algebra Examples

$3 x^{2} - 9 x + 4 = 0$

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 $a = 3$ , $b = - 9$ , and $c = 4$ into the quadratic formula and solve for $x$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (3 \cdot 4)}}{2 \cdot 3}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise $- 9$ to the power of $2$ .

$x = \frac{9 \pm \sqrt{81 - 4 \cdot 3 \cdot 4}}{2 \cdot 3}$

Step 3.1.2

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

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Step 3.1.2.1

Multiply $- 4$ by $3$ .

$x = \frac{9 \pm \sqrt{81 - 12 \cdot 4}}{2 \cdot 3}$

Step 3.1.2.2

Multiply $- 12$ by $4$ .

$x = \frac{9 \pm \sqrt{81 - 48}}{2 \cdot 3}$

Step 3.1.3

Subtract $48$ from $81$ .

$x = \frac{9 \pm \sqrt{33}}{2 \cdot 3}$

Step 3.2

Multiply $2$ by $3$ .

$x = \frac{9 \pm \sqrt{33}}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9 \pm \sqrt{33}}{6}$

Decimal Form:

$x = 2.45742710 \dots, 0.54257289 \dots$