Algebra Examples

$15 = 8 x^{2} - 14 x$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $8 x^{2}$ from both sides of the equation.

$15 - 8 x^{2} = - 14 x$

Step 1.2

Add $14 x$ to both sides of the equation.

$15 - 8 x^{2} + 14 x = 0$

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 $a = - 8$ , $b = 14$ , and $c = 15$ into the quadratic formula and solve for $x$ .

$\frac{- 14 \pm \sqrt{14^{2} - 4 \cdot (- 8 \cdot 15)}}{2 \cdot - 8}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $14$ to the power of $2$ .

$x = \frac{- 14 \pm \sqrt{196 - 4 \cdot - 8 \cdot 15}}{2 \cdot - 8}$

Step 4.1.2

Multiply $- 4 \cdot - 8 \cdot 15$ .

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Step 4.1.2.1

Multiply $- 4$ by $- 8$ .

$x = \frac{- 14 \pm \sqrt{196 + 32 \cdot 15}}{2 \cdot - 8}$

Step 4.1.2.2

Multiply $32$ by $15$ .

$x = \frac{- 14 \pm \sqrt{196 + 480}}{2 \cdot - 8}$

Step 4.1.3

Add $196$ and $480$ .

$x = \frac{- 14 \pm \sqrt{676}}{2 \cdot - 8}$

Step 4.1.4

Rewrite $676$ as $26^{2}$ .

$x = \frac{- 14 \pm \sqrt{26^{2}}}{2 \cdot - 8}$

Step 4.1.5

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

$x = \frac{- 14 \pm 26}{2 \cdot - 8}$

Step 4.2

Multiply $2$ by $- 8$ .

$x = \frac{- 14 \pm 26}{- 16}$

Step 4.3

Simplify $\frac{- 14 \pm 26}{- 16}$ .

$x = \frac{7 \pm 13}{8}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{5}{2}, - \frac{3}{4}$