Algebra Examples

$4 p^{2} = 12 p - 5$

Step 1

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

Tap for more steps...

Step 1.1

Subtract $12 p$ from both sides of the equation.

$4 p^{2} - 12 p = - 5$

Step 1.2

Add $5$ to both sides of the equation.

$4 p^{2} - 12 p + 5 = 0$

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 $a = 4$ , $b = - 12$ , and $c = 5$ into the quadratic formula and solve for $p$ .

$\frac{12 \pm \sqrt{{(- 12)}^{2} - 4 \cdot (4 \cdot 5)}}{2 \cdot 4}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Raise $- 12$ to the power of $2$ .

$p = \frac{12 \pm \sqrt{144 - 4 \cdot 4 \cdot 5}}{2 \cdot 4}$

Step 4.1.2

Multiply $- 4 \cdot 4 \cdot 5$ .

Tap for more steps...

Step 4.1.2.1

Multiply $- 4$ by $4$ .

$p = \frac{12 \pm \sqrt{144 - 16 \cdot 5}}{2 \cdot 4}$

Step 4.1.2.2

Multiply $- 16$ by $5$ .

$p = \frac{12 \pm \sqrt{144 - 80}}{2 \cdot 4}$

Step 4.1.3

Subtract $80$ from $144$ .

$p = \frac{12 \pm \sqrt{64}}{2 \cdot 4}$

Step 4.1.4

Rewrite $64$ as $8^{2}$ .

$p = \frac{12 \pm \sqrt{8^{2}}}{2 \cdot 4}$

Step 4.1.5

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

$p = \frac{12 \pm 8}{2 \cdot 4}$

Step 4.2

Multiply $2$ by $4$ .

$p = \frac{12 \pm 8}{8}$

Step 4.3

Simplify $\frac{12 \pm 8}{8}$ .

$p = \frac{3 \pm 2}{2}$

Step 5

The final answer is the combination of both solutions.

$p = \frac{5}{2}, \frac{1}{2}$