Calculus Examples

$3 x^{2} - 26 x + 48 x = 6$

Step 1

Add $- 26 x$ and $48 x$ .

$3 x^{2} + 22 x = 6$

Step 2

Subtract $6$ from both sides of the equation.

$3 x^{2} + 22 x - 6 = 0$

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

Substitute the values $a = 3$ , $b = 22$ , and $c = - 6$ into the quadratic formula and solve for $x$ .

$\frac{- 22 \pm \sqrt{22^{2} - 4 \cdot (3 \cdot - 6)}}{2 \cdot 3}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Raise $22$ to the power of $2$ .

$x = \frac{- 22 \pm \sqrt{484 - 4 \cdot 3 \cdot - 6}}{2 \cdot 3}$

Step 5.1.2

Multiply $- 4 \cdot 3 \cdot - 6$ .

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Step 5.1.2.1

Multiply $- 4$ by $3$ .

$x = \frac{- 22 \pm \sqrt{484 - 12 \cdot - 6}}{2 \cdot 3}$

Step 5.1.2.2

Multiply $- 12$ by $- 6$ .

$x = \frac{- 22 \pm \sqrt{484 + 72}}{2 \cdot 3}$

Step 5.1.3

Add $484$ and $72$ .

$x = \frac{- 22 \pm \sqrt{556}}{2 \cdot 3}$

Step 5.1.4

Rewrite $556$ as $2^{2} \cdot 139$ .

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Step 5.1.4.1

Factor $4$ out of $556$ .

$x = \frac{- 22 \pm \sqrt{4 (139)}}{2 \cdot 3}$

Step 5.1.4.2

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 22 \pm \sqrt{2^{2} \cdot 139}}{2 \cdot 3}$

Step 5.1.5

Pull terms out from under the radical.

$x = \frac{- 22 \pm 2 \sqrt{139}}{2 \cdot 3}$

Step 5.2

Multiply $2$ by $3$ .

$x = \frac{- 22 \pm 2 \sqrt{139}}{6}$

Step 5.3

Simplify $\frac{- 22 \pm 2 \sqrt{139}}{6}$ .

$x = \frac{- 11 \pm \sqrt{139}}{3}$

Step 6

The final answer is the combination of both solutions.

$x = - \frac{11 - \sqrt{139}}{3}, - \frac{11 + \sqrt{139}}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{11 - \sqrt{139}}{3}, - \frac{11 + \sqrt{139}}{3}$

Decimal Form:

$x = 0.26327537 \dots, - 7.59660870 \dots$