Algebra Examples

$6 x^{2} - 13 x = - 6$

Step 1

Add $6$ to both sides of the equation.

$6 x^{2} - 13 x + 6 = 0$

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 $a = 6$ , $b = - 13$ , and $c = 6$ into the quadratic formula and solve for $x$ .

$\frac{13 \pm \sqrt{{(- 13)}^{2} - 4 \cdot (6 \cdot 6)}}{2 \cdot 6}$

Step 4

Simplify.

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Simplify the numerator.

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Raise $- 13$ to the power of $2$ .

$x = \frac{13 \pm \sqrt{169 - 4 \cdot 6 \cdot 6}}{2 \cdot 6}$

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

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Multiply $- 4$ by $6$ .

$x = \frac{13 \pm \sqrt{169 - 24 \cdot 6}}{2 \cdot 6}$

Multiply $- 24$ by $6$ .

$x = \frac{13 \pm \sqrt{169 - 144}}{2 \cdot 6}$

Subtract $144$ from $169$ .

$x = \frac{13 \pm \sqrt{25}}{2 \cdot 6}$

Rewrite $25$ as $5^{2}$ .

$x = \frac{13 \pm \sqrt{5^{2}}}{2 \cdot 6}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{13 \pm 5}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{13 \pm 5}{12}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{3}{2}, \frac{2}{3}$