Algebra Examples

$9 x + 2 = 8 x^{2} + 6 x$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$8 x^{2} + 6 x = 9 x + 2$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Subtract $9 x$ from both sides of the equation.

$8 x^{2} + 6 x - 9 x = 2$

Step 2.2

Subtract $9 x$ from $6 x$ .

$8 x^{2} - 3 x = 2$

Step 3

Subtract $2$ from both sides of the equation.

$8 x^{2} - 3 x - 2 = 0$

Step 4

Use the quadratic formula to find the solutions.

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

Step 5

Substitute the values $a = 8$ , $b = - 3$ , and $c = - 2$ into the quadratic formula and solve for $x$ .

$\frac{3 \pm \sqrt{{(- 3)}^{2} - 4 \cdot (8 \cdot - 2)}}{2 \cdot 8}$

Step 6

Simplify.

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Step 6.1

Simplify the numerator.

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Step 6.1.1

Raise $- 3$ to the power of $2$ .

$x = \frac{3 \pm \sqrt{9 - 4 \cdot 8 \cdot - 2}}{2 \cdot 8}$

Step 6.1.2

Multiply $- 4 \cdot 8 \cdot - 2$ .

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Step 6.1.2.1

Multiply $- 4$ by $8$ .

$x = \frac{3 \pm \sqrt{9 - 32 \cdot - 2}}{2 \cdot 8}$

Step 6.1.2.2

Multiply $- 32$ by $- 2$ .

$x = \frac{3 \pm \sqrt{9 + 64}}{2 \cdot 8}$

Step 6.1.3

Add $9$ and $64$ .

$x = \frac{3 \pm \sqrt{73}}{2 \cdot 8}$

Step 6.2

Multiply $2$ by $8$ .

$x = \frac{3 \pm \sqrt{73}}{16}$

Step 7

The final answer is the combination of both solutions.

$x = \frac{3 + \sqrt{73}}{16}, \frac{3 - \sqrt{73}}{16}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3 + \sqrt{73}}{16}, \frac{3 - \sqrt{73}}{16}$

Decimal Form:

$x = 0.72150023 \dots, - 0.34650023 \dots$