Solve Using the Quadratic Formula 12y^2+40y=7

$12 y^{2} + 40 y = 7$

Step 1

Subtract $7$ from both sides of the equation.

$12 y^{2} + 40 y - 7 = 0$

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 $a = 12$ , $b = 40$ , and $c = - 7$ into the quadratic formula and solve for $y$ .

$\frac{- 40 \pm \sqrt{40^{2} - 4 \cdot (12 \cdot - 7)}}{2 \cdot 12}$

Step 4

Simplify.

Simplify the numerator.

Raise $40$ to the power of $2$ .

$y = \frac{- 40 \pm \sqrt{1600 - 4 \cdot 12 \cdot - 7}}{2 \cdot 12}$

Multiply $- 4 \cdot 12 \cdot - 7$ .

Multiply $- 4$ by $12$ .

$y = \frac{- 40 \pm \sqrt{1600 - 48 \cdot - 7}}{2 \cdot 12}$

Multiply $- 48$ by $- 7$ .

$y = \frac{- 40 \pm \sqrt{1600 + 336}}{2 \cdot 12}$

Add $1600$ and $336$ .

$y = \frac{- 40 \pm \sqrt{1936}}{2 \cdot 12}$

Rewrite $1936$ as $44^{2}$ .

$y = \frac{- 40 \pm \sqrt{44^{2}}}{2 \cdot 12}$

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

$y = \frac{- 40 \pm 44}{2 \cdot 12}$

Multiply $2$ by $12$ .

$y = \frac{- 40 \pm 44}{24}$

Simplify $\frac{- 40 \pm 44}{24}$ .

$y = \frac{- 10 \pm 11}{6}$

Step 5

The final answer is the combination of both solutions.

$y = \frac{1}{6}, - \frac{7}{2}$