Solve Using the Quadratic Formula 17x^2=12x

$17 x^{2} = 12 x$

Step 1

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

$17 x^{2} - 12 x = 0$

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 $a = 17$ , $b = - 12$ , and $c = 0$ into the quadratic formula and solve for $x$ .

$\frac{12 \pm \sqrt{{(- 12)}^{2} - 4 \cdot (17 \cdot 0)}}{2 \cdot 17}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{12 \pm \sqrt{144 - 4 \cdot 17 \cdot 0}}{2 \cdot 17}$

Multiply $- 4 \cdot 17 \cdot 0$ .

Multiply $- 4$ by $17$ .

$x = \frac{12 \pm \sqrt{144 - 68 \cdot 0}}{2 \cdot 17}$

Multiply $- 68$ by $0$ .

$x = \frac{12 \pm \sqrt{144 + 0}}{2 \cdot 17}$

Add $144$ and $0$ .

$x = \frac{12 \pm \sqrt{144}}{2 \cdot 17}$

Rewrite $144$ as $12^{2}$ .

$x = \frac{12 \pm \sqrt{12^{2}}}{2 \cdot 17}$

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

$x = \frac{12 \pm 12}{2 \cdot 17}$

Multiply $2$ by $17$ .

$x = \frac{12 \pm 12}{34}$

Simplify $\frac{12 \pm 12}{34}$ .

$x = \frac{6 \pm 6}{17}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{12}{17}, 0$