Solve Using the Quadratic Formula 6x^2+11x=72

$6 x^{2} + 11 x = 72$

Step 1

Subtract $72$ from both sides of the equation.

$6 x^{2} + 11 x - 72 = 0$

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 $a = 6$ , $b = 11$ , and $c = - 72$ into the quadratic formula and solve for $x$ .

$\frac{- 11 \pm \sqrt{11^{2} - 4 \cdot (6 \cdot - 72)}}{2 \cdot 6}$

Step 4

Simplify.

Simplify the numerator.

Raise $11$ to the power of $2$ .

$x = \frac{- 11 \pm \sqrt{121 - 4 \cdot 6 \cdot - 72}}{2 \cdot 6}$

Multiply $- 4 \cdot 6 \cdot - 72$ .

Multiply $- 4$ by $6$ .

$x = \frac{- 11 \pm \sqrt{121 - 24 \cdot - 72}}{2 \cdot 6}$

Multiply $- 24$ by $- 72$ .

$x = \frac{- 11 \pm \sqrt{121 + 1728}}{2 \cdot 6}$

Add $121$ and $1728$ .

$x = \frac{- 11 \pm \sqrt{1849}}{2 \cdot 6}$

Rewrite $1849$ as $43^{2}$ .

$x = \frac{- 11 \pm \sqrt{43^{2}}}{2 \cdot 6}$

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

$x = \frac{- 11 \pm 43}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{- 11 \pm 43}{12}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{8}{3}, - \frac{9}{2}$