Finite Math Examples

$3 x^{2} - 9 x = 7$

Step 1

Subtract $7$ from both sides of the equation.

$3 x^{2} - 9 x - 7 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 3$ , $b = - 9$ , and $c = - 7$ into the quadratic formula and solve for $x$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (3 \cdot - 7)}}{2 \cdot 3}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

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

$x = \frac{9 \pm \sqrt{81 - 4 \cdot 3 \cdot - 7}}{2 \cdot 3}$

Step 4.1.2

Multiply $- 4 \cdot 3 \cdot - 7$ .

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Step 4.1.2.1

Multiply $- 4$ by $3$ .

$x = \frac{9 \pm \sqrt{81 - 12 \cdot - 7}}{2 \cdot 3}$

Step 4.1.2.2

Multiply $- 12$ by $- 7$ .

$x = \frac{9 \pm \sqrt{81 + 84}}{2 \cdot 3}$

Step 4.1.3

Add $81$ and $84$ .

$x = \frac{9 \pm \sqrt{165}}{2 \cdot 3}$

Step 4.2

Multiply $2$ by $3$ .

$x = \frac{9 \pm \sqrt{165}}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9 \pm \sqrt{165}}{6}$

Decimal Form:

$x = 3.64087209 \dots, - 0.64087209 \dots$