Solve Using the Quadratic Formula 7p^2=-6p+3

$7 p^{2} = - 6 p + 3$

Step 1

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

Add $6 p$ to both sides of the equation.

$7 p^{2} + 6 p = 3$

Subtract $3$ from both sides of the equation.

$7 p^{2} + 6 p - 3 = 0$

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 $a = 7$ , $b = 6$ , and $c = - 3$ into the quadratic formula and solve for $p$ .

$\frac{- 6 \pm \sqrt{6^{2} - 4 \cdot (7 \cdot - 3)}}{2 \cdot 7}$

Step 4

Simplify.

Simplify the numerator.

Raise $6$ to the power of $2$ .

$p = \frac{- 6 \pm \sqrt{36 - 4 \cdot 7 \cdot - 3}}{2 \cdot 7}$

Multiply $- 4 \cdot 7 \cdot - 3$ .

Multiply $- 4$ by $7$ .

$p = \frac{- 6 \pm \sqrt{36 - 28 \cdot - 3}}{2 \cdot 7}$

Multiply $- 28$ by $- 3$ .

$p = \frac{- 6 \pm \sqrt{36 + 84}}{2 \cdot 7}$

Add $36$ and $84$ .

$p = \frac{- 6 \pm \sqrt{120}}{2 \cdot 7}$

Rewrite $120$ as $2^{2} \cdot 30$ .

Factor $4$ out of $120$ .

$p = \frac{- 6 \pm \sqrt{4 (30)}}{2 \cdot 7}$

Rewrite $4$ as $2^{2}$ .

$p = \frac{- 6 \pm \sqrt{2^{2} \cdot 30}}{2 \cdot 7}$

Pull terms out from under the radical.

$p = \frac{- 6 \pm 2 \sqrt{30}}{2 \cdot 7}$

Multiply $2$ by $7$ .

$p = \frac{- 6 \pm 2 \sqrt{30}}{14}$

Simplify $\frac{- 6 \pm 2 \sqrt{30}}{14}$ .

$p = \frac{- 3 \pm \sqrt{30}}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$p = \frac{- 3 \pm \sqrt{30}}{7}$

Decimal Form:

$p = 0.35388936 \dots, - 1.21103222 \dots$