Solve Using the Quadratic Formula 7x+1=3x^2-2x+1

$7 x + 1 = 3 x^{2} - 2 x + 1$

Step 1

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

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

Subtract $3 x^{2}$ from both sides of the equation.

$7 x + 1 - 3 x^{2} = - 2 x + 1$

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

$7 x + 1 - 3 x^{2} + 2 x = 1$

Subtract $1$ from both sides of the equation.

$7 x + 1 - 3 x^{2} + 2 x - 1 = 0$

Simplify $7 x + 1 - 3 x^{2} + 2 x - 1$ .

Combine the opposite terms in $7 x + 1 - 3 x^{2} + 2 x - 1$ .

Subtract $1$ from $1$ .

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

Add $7 x - 3 x^{2} + 2 x$ and $0$ .

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

Add $7 x$ and $2 x$ .

$- 3 x^{2} + 9 x = 0$

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 $a = - 3$ , $b = 9$ , and $c = 0$ into the quadratic formula and solve for $x$ .

$\frac{- 9 \pm \sqrt{9^{2} - 4 \cdot (- 3 \cdot 0)}}{2 \cdot - 3}$

Step 4

Simplify.

Simplify the numerator.

Raise $9$ to the power of $2$ .

$x = \frac{- 9 \pm \sqrt{81 - 4 \cdot - 3 \cdot 0}}{2 \cdot - 3}$

Multiply $- 4 \cdot - 3 \cdot 0$ .

Multiply $- 4$ by $- 3$ .

$x = \frac{- 9 \pm \sqrt{81 + 12 \cdot 0}}{2 \cdot - 3}$

Multiply $12$ by $0$ .

$x = \frac{- 9 \pm \sqrt{81 + 0}}{2 \cdot - 3}$

Add $81$ and $0$ .

$x = \frac{- 9 \pm \sqrt{81}}{2 \cdot - 3}$

Rewrite $81$ as $9^{2}$ .

$x = \frac{- 9 \pm \sqrt{9^{2}}}{2 \cdot - 3}$

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

$x = \frac{- 9 \pm 9}{2 \cdot - 3}$

Multiply $2$ by $- 3$ .

$x = \frac{- 9 \pm 9}{- 6}$

Simplify $\frac{- 9 \pm 9}{- 6}$ .

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

Step 5

The final answer is the combination of both solutions.

$x = 3, 0$

Solve Using the Quadratic Formula 7x+1=3x^2-2x+1

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