Solve Using the Quadratic Formula 6x^2-5x=56

$6 x^{2} - 5 x = 56$

Step 1

Subtract $56$ from both sides of the equation.

$6 x^{2} - 5 x - 56 = 0$

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 $a = 6$ , $b = - 5$ , and $c = - 56$ into the quadratic formula and solve for $x$ .

$\frac{5 \pm \sqrt{{(- 5)}^{2} - 4 \cdot (6 \cdot - 56)}}{2 \cdot 6}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 5$ to the power of $2$ .

$x = \frac{5 \pm \sqrt{25 - 4 \cdot 6 \cdot - 56}}{2 \cdot 6}$

Multiply $- 4 \cdot 6 \cdot - 56$ .

Multiply $- 4$ by $6$ .

$x = \frac{5 \pm \sqrt{25 - 24 \cdot - 56}}{2 \cdot 6}$

Multiply $- 24$ by $- 56$ .

$x = \frac{5 \pm \sqrt{25 + 1344}}{2 \cdot 6}$

Add $25$ and $1344$ .

$x = \frac{5 \pm \sqrt{1369}}{2 \cdot 6}$

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

$x = \frac{5 \pm \sqrt{37^{2}}}{2 \cdot 6}$

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

$x = \frac{5 \pm 37}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{5 \pm 37}{12}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{7}{2}, - \frac{8}{3}$