Algebra Examples

$6 x^{2} - 2 x = 7$

Step 1

Subtract $7$ from both sides of the equation.

$6 x^{2} - 2 x - 7 = 0$

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 $a = 6$ , $b = - 2$ , and $c = - 7$ into the quadratic formula and solve for $x$ .

$\frac{2 \pm \sqrt{{(- 2)}^{2} - 4 \cdot (6 \cdot - 7)}}{2 \cdot 6}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

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

$x = \frac{2 \pm \sqrt{4 - 4 \cdot 6 \cdot - 7}}{2 \cdot 6}$

Step 4.1.2

Multiply $- 4 \cdot 6 \cdot - 7$ .

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Step 4.1.2.1

Multiply $- 4$ by $6$ .

$x = \frac{2 \pm \sqrt{4 - 24 \cdot - 7}}{2 \cdot 6}$

Step 4.1.2.2

Multiply $- 24$ by $- 7$ .

$x = \frac{2 \pm \sqrt{4 + 168}}{2 \cdot 6}$

Step 4.1.3

Add $4$ and $168$ .

$x = \frac{2 \pm \sqrt{172}}{2 \cdot 6}$

Step 4.1.4

Rewrite $172$ as $2^{2} \cdot 43$ .

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Step 4.1.4.1

Factor $4$ out of $172$ .

$x = \frac{2 \pm \sqrt{4 (43)}}{2 \cdot 6}$

Step 4.1.4.2

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

$x = \frac{2 \pm \sqrt{2^{2} \cdot 43}}{2 \cdot 6}$

Step 4.1.5

Pull terms out from under the radical.

$x = \frac{2 \pm 2 \sqrt{43}}{2 \cdot 6}$

Step 4.2

Multiply $2$ by $6$ .

$x = \frac{2 \pm 2 \sqrt{43}}{12}$

Step 4.3

Simplify $\frac{2 \pm 2 \sqrt{43}}{12}$ .

$x = \frac{1 \pm \sqrt{43}}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1 \pm \sqrt{43}}{6}$

Decimal Form:

$x = 1.25957308 \dots, - 0.92623975 \dots$