Finite Math Examples

$p = 3 x^{2} - 17 x + 20$

Step 1

Rewrite the equation as $3 x^{2} - 17 x + 20 = p$ .

$3 x^{2} - 17 x + 20 = p$

Step 2

Subtract $p$ from both sides of the equation.

$3 x^{2} - 17 x + 20 - p = 0$

Step 3

Use the quadratic formula to find the solutions.

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

Step 4

Substitute the values $a = 3$ , $b = - 17$ , and $c = 20 - p$ into the quadratic formula and solve for $x$ .

$\frac{17 \pm \sqrt{{(- 17)}^{2} - 4 \cdot (3 \cdot (20 - p))}}{2 \cdot 3}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

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

$x = \frac{17 \pm \sqrt{289 - 4 \cdot 3 \cdot (20 - p)}}{2 \cdot 3}$

Step 5.1.2

Multiply $- 4$ by $3$ .

$x = \frac{17 \pm \sqrt{289 - 12 \cdot (20 - p)}}{2 \cdot 3}$

Step 5.1.3

Apply the distributive property.

$x = \frac{17 \pm \sqrt{289 - 12 \cdot 20 - 12 (- p)}}{2 \cdot 3}$

Step 5.1.4

Multiply $- 12$ by $20$ .

$x = \frac{17 \pm \sqrt{289 - 240 - 12 (- p)}}{2 \cdot 3}$

Step 5.1.5

Multiply $- 1$ by $- 12$ .

$x = \frac{17 \pm \sqrt{289 - 240 + 12 p}}{2 \cdot 3}$

Step 5.1.6

Subtract $240$ from $289$ .

$x = \frac{17 \pm \sqrt{49 + 12 p}}{2 \cdot 3}$

Step 5.2

Multiply $2$ by $3$ .

$x = \frac{17 \pm \sqrt{49 + 12 p}}{6}$

Step 6

The final answer is the combination of both solutions.

$x = \frac{17 + \sqrt{49 + 12 p}}{6}$

$x = \frac{17 - \sqrt{49 + 12 p}}{6}$