Finite Math Examples

$2 n^{2} + 5 n - 9 = 0$

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 $a = 2$ , $b = 5$ , and $c = - 9$ into the quadratic formula and solve for $n$ .

$\frac{- 5 \pm \sqrt{5^{2} - 4 \cdot (2 \cdot - 9)}}{2 \cdot 2}$

Step 3

Simplify.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise $5$ to the power of $2$ .

$n = \frac{- 5 \pm \sqrt{25 - 4 \cdot 2 \cdot - 9}}{2 \cdot 2}$

Step 3.1.2

Multiply $- 4 \cdot 2 \cdot - 9$ .

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Step 3.1.2.1

Multiply $- 4$ by $2$ .

$n = \frac{- 5 \pm \sqrt{25 - 8 \cdot - 9}}{2 \cdot 2}$

Step 3.1.2.2

Multiply $- 8$ by $- 9$ .

$n = \frac{- 5 \pm \sqrt{25 + 72}}{2 \cdot 2}$

Step 3.1.3

Add $25$ and $72$ .

$n = \frac{- 5 \pm \sqrt{97}}{2 \cdot 2}$

Step 3.2

Multiply $2$ by $2$ .

$n = \frac{- 5 \pm \sqrt{97}}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$n = \frac{- 5 \pm \sqrt{97}}{4}$

Decimal Form:

$n = 1.21221445 \dots, - 3.71221445 \dots$