Solve Using the Quadratic Formula 6x^2+17x=45

$6 x^{2} + 17 x = 45$

Step 1

Subtract $45$ from both sides of the equation.

$6 x^{2} + 17 x - 45 = 0$

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 $a = 6$ , $b = 17$ , and $c = - 45$ into the quadratic formula and solve for $x$ .

$\frac{- 17 \pm \sqrt{17^{2} - 4 \cdot (6 \cdot - 45)}}{2 \cdot 6}$

Step 4

Simplify.

Simplify the numerator.

Raise $17$ to the power of $2$ .

$x = \frac{- 17 \pm \sqrt{289 - 4 \cdot 6 \cdot - 45}}{2 \cdot 6}$

Multiply $- 4 \cdot 6 \cdot - 45$ .

Multiply $- 4$ by $6$ .

$x = \frac{- 17 \pm \sqrt{289 - 24 \cdot - 45}}{2 \cdot 6}$

Multiply $- 24$ by $- 45$ .

$x = \frac{- 17 \pm \sqrt{289 + 1080}}{2 \cdot 6}$

Add $289$ and $1080$ .

$x = \frac{- 17 \pm \sqrt{1369}}{2 \cdot 6}$

Rewrite $1369$ as $37^{2}$ .

$x = \frac{- 17 \pm \sqrt{37^{2}}}{2 \cdot 6}$

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

$x = \frac{- 17 \pm 37}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{- 17 \pm 37}{12}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{5}{3}, - \frac{9}{2}$