Solve Using the Quadratic Formula 7x^2-10x+9=5-2x

$7 x^{2} - 10 x + 9 = 5 - 2 x$

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

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

Subtract $5$ from both sides of the equation.

$7 x^{2} - 10 x + 9 - 5 = - 2 x$

Add $2 x$ to both sides of the equation.

$7 x^{2} - 10 x + 9 - 5 + 2 x = 0$

Simplify $7 x^{2} - 10 x + 9 - 5 + 2 x$ .

Add $- 10 x$ and $2 x$ .

$7 x^{2} - 8 x + 9 - 5 = 0$

Subtract $5$ from $9$ .

$7 x^{2} - 8 x + 4 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 7$ , $b = - 8$ , and $c = 4$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (7 \cdot 4)}}{2 \cdot 7}$

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 7 \cdot 4}}{2 \cdot 7}$

Multiply $- 4$ by $7$ .

$x = \frac{8 \pm \sqrt{64 - 28 \cdot 4}}{2 \cdot 7}$

Multiply $- 28$ by $4$ .

$x = \frac{8 \pm \sqrt{64 - 112}}{2 \cdot 7}$

Subtract $112$ from $64$ .

$x = \frac{8 \pm \sqrt{- 48}}{2 \cdot 7}$

Rewrite $- 48$ as $- 1 (48)$ .

$x = \frac{8 \pm \sqrt{- 1 \cdot 48}}{2 \cdot 7}$

Rewrite $\sqrt{- 1 (48)}$ as $\sqrt{- 1} \cdot \sqrt{48}$ .

$x = \frac{8 \pm \sqrt{- 1} \cdot \sqrt{48}}{2 \cdot 7}$

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

$x = \frac{8 \pm i \cdot \sqrt{48}}{2 \cdot 7}$

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$x = \frac{8 \pm i \cdot \sqrt{16 (3)}}{2 \cdot 7}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{8 \pm i \cdot \sqrt{4^{2} \cdot 3}}{2 \cdot 7}$

Pull terms out from under the radical.

$x = \frac{8 \pm i \cdot (4 \sqrt{3})}{2 \cdot 7}$

Move $4$ to the left of $i$ .

$x = \frac{8 \pm 4 i \sqrt{3}}{2 \cdot 7}$

Multiply $2$ by $7$ .

$x = \frac{8 \pm 4 i \sqrt{3}}{14}$

Simplify $\frac{8 \pm 4 i \sqrt{3}}{14}$ .

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