Solve Using the Quadratic Formula 3x^2+2x=7

$3 x^{2} + 2 x = 7$

Step 1

Subtract $7$ from both sides of the equation.

$3 x^{2} + 2 x - 7 = 0$

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 $a = 3$ , $b = 2$ , and $c = - 7$ into the quadratic formula and solve for $x$ .

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

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 2 \pm \sqrt{4 - 4 \cdot 3 \cdot - 7}}{2 \cdot 3}$

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

Multiply $- 4$ by $3$ .

$x = \frac{- 2 \pm \sqrt{4 - 12 \cdot - 7}}{2 \cdot 3}$

Multiply $- 12$ by $- 7$ .

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

Add $4$ and $84$ .

$x = \frac{- 2 \pm \sqrt{88}}{2 \cdot 3}$

Rewrite $88$ as $2^{2} \cdot 22$ .

Factor $4$ out of $88$ .

$x = \frac{- 2 \pm \sqrt{4 (22)}}{2 \cdot 3}$

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

$x = \frac{- 2 \pm \sqrt{2^{2} \cdot 22}}{2 \cdot 3}$

Pull terms out from under the radical.

$x = \frac{- 2 \pm 2 \sqrt{22}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 2 \pm 2 \sqrt{22}}{6}$

Simplify $\frac{- 2 \pm 2 \sqrt{22}}{6}$ .

$x = \frac{- 1 \pm \sqrt{22}}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 1 \pm \sqrt{22}}{3}$

Decimal Form:

$x = 1.23013858 \dots, - 1.89680525 \dots$