Finite Math Examples

$6 x + 3 x^{2} - \frac{50}{5} = 20 x + 3 x - 94$

Step 1

Simplify each term.

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Step 1.1

Divide $50$ by $5$ .

$6 x + 3 x^{2} - 1 \cdot 10 = 20 x + 3 x - 94$

Step 1.2

Multiply $- 1$ by $10$ .

$6 x + 3 x^{2} - 10 = 20 x + 3 x - 94$

Step 2

Add $20 x$ and $3 x$ .

$6 x + 3 x^{2} - 10 = 23 x - 94$

Step 3

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

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Step 3.1

Subtract $23 x$ from both sides of the equation.

$6 x + 3 x^{2} - 10 - 23 x = - 94$

Step 3.2

Subtract $23 x$ from $6 x$ .

$- 17 x + 3 x^{2} - 10 = - 94$

Step 4

Move all terms to the left side of the equation and simplify.

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Step 4.1

Add $94$ to both sides of the equation.

$- 17 x + 3 x^{2} - 10 + 94 = 0$

Step 4.2

Add $- 10$ and $94$ .

$- 17 x + 3 x^{2} + 84 = 0$

Step 5

Use the quadratic formula to find the solutions.

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

Step 6

Substitute the values $a = 3$ , $b = - 17$ , and $c = 84$ into the quadratic formula and solve for $x$ .

$\frac{17 \pm \sqrt{{(- 17)}^{2} - 4 \cdot (3 \cdot 84)}}{2 \cdot 3}$

Step 7

Simplify.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Raise $- 17$ to the power of $2$ .

$x = \frac{17 \pm \sqrt{289 - 4 \cdot 3 \cdot 84}}{2 \cdot 3}$

Step 7.1.2

Multiply $- 4 \cdot 3 \cdot 84$ .

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Step 7.1.2.1

Multiply $- 4$ by $3$ .

$x = \frac{17 \pm \sqrt{289 - 12 \cdot 84}}{2 \cdot 3}$

Step 7.1.2.2

Multiply $- 12$ by $84$ .

$x = \frac{17 \pm \sqrt{289 - 1008}}{2 \cdot 3}$

Step 7.1.3

Subtract $1008$ from $289$ .

$x = \frac{17 \pm \sqrt{- 719}}{2 \cdot 3}$

Step 7.1.4

Rewrite $- 719$ as $- 1 (719)$ .

$x = \frac{17 \pm \sqrt{- 1 \cdot 719}}{2 \cdot 3}$

Step 7.1.5

Rewrite $\sqrt{- 1 (719)}$ as $\sqrt{- 1} \cdot \sqrt{719}$ .

$x = \frac{17 \pm \sqrt{- 1} \cdot \sqrt{719}}{2 \cdot 3}$

Step 7.1.6

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{17 \pm i \sqrt{719}}{2 \cdot 3}$

Step 7.2

Multiply $2$ by $3$ .

$x = \frac{17 \pm i \sqrt{719}}{6}$

Step 8

The final answer is the combination of both solutions.

$x = \frac{17 + i \sqrt{719}}{6}, \frac{17 - i \sqrt{719}}{6}$