Basic Math Examples

$6 y^{2} - 7 y = 2$

Step 1

Subtract $2$ from both sides of the equation.

$6 y^{2} - 7 y - 2 = 0$

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 $a = 6$ , $b = - 7$ , and $c = - 2$ into the quadratic formula and solve for $y$ .

$\frac{7 \pm \sqrt{{(- 7)}^{2} - 4 \cdot (6 \cdot - 2)}}{2 \cdot 6}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Raise $- 7$ to the power of $2$ .

$y = \frac{7 \pm \sqrt{49 - 4 \cdot 6 \cdot - 2}}{2 \cdot 6}$

Step 4.1.2

Multiply $- 4 \cdot 6 \cdot - 2$ .

Tap for more steps...

Step 4.1.2.1

Multiply $- 4$ by $6$ .

$y = \frac{7 \pm \sqrt{49 - 24 \cdot - 2}}{2 \cdot 6}$

Step 4.1.2.2

Multiply $- 24$ by $- 2$ .

$y = \frac{7 \pm \sqrt{49 + 48}}{2 \cdot 6}$

Step 4.1.3

Add $49$ and $48$ .

$y = \frac{7 \pm \sqrt{97}}{2 \cdot 6}$

Step 4.2

Multiply $2$ by $6$ .

$y = \frac{7 \pm \sqrt{97}}{12}$

Step 5

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Tap for more steps...

Step 5.1

Simplify the numerator.

Tap for more steps...

Step 5.1.1

Raise $- 7$ to the power of $2$ .

$y = \frac{7 \pm \sqrt{49 - 4 \cdot 6 \cdot - 2}}{2 \cdot 6}$

Step 5.1.2

Multiply $- 4 \cdot 6 \cdot - 2$ .

Tap for more steps...

Step 5.1.2.1

Multiply $- 4$ by $6$ .

$y = \frac{7 \pm \sqrt{49 - 24 \cdot - 2}}{2 \cdot 6}$

Step 5.1.2.2

Multiply $- 24$ by $- 2$ .

$y = \frac{7 \pm \sqrt{49 + 48}}{2 \cdot 6}$

Step 5.1.3

Add $49$ and $48$ .

$y = \frac{7 \pm \sqrt{97}}{2 \cdot 6}$

Step 5.2

Multiply $2$ by $6$ .

$y = \frac{7 \pm \sqrt{97}}{12}$

Step 5.3

Change the $\pm$ to $+$ .

$y = \frac{7 + \sqrt{97}}{12}$

Step 6

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Tap for more steps...

Step 6.1

Simplify the numerator.

Tap for more steps...

Step 6.1.1

Raise $- 7$ to the power of $2$ .

$y = \frac{7 \pm \sqrt{49 - 4 \cdot 6 \cdot - 2}}{2 \cdot 6}$

Step 6.1.2

Multiply $- 4 \cdot 6 \cdot - 2$ .

Tap for more steps...

Step 6.1.2.1

Multiply $- 4$ by $6$ .

$y = \frac{7 \pm \sqrt{49 - 24 \cdot - 2}}{2 \cdot 6}$

Step 6.1.2.2

Multiply $- 24$ by $- 2$ .

$y = \frac{7 \pm \sqrt{49 + 48}}{2 \cdot 6}$

Step 6.1.3

Add $49$ and $48$ .

$y = \frac{7 \pm \sqrt{97}}{2 \cdot 6}$

Step 6.2

Multiply $2$ by $6$ .

$y = \frac{7 \pm \sqrt{97}}{12}$

Step 6.3

Change the $\pm$ to $-$ .

$y = \frac{7 - \sqrt{97}}{12}$

Step 7

The final answer is the combination of both solutions.

$y = \frac{7 + \sqrt{97}}{12}, \frac{7 - \sqrt{97}}{12}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$y = \frac{7 + \sqrt{97}}{12}, \frac{7 - \sqrt{97}}{12}$

Decimal Form:

$y = 1.40407148 \dots, - 0.23740481 \dots$