Finite Math Examples

$8 y = 5 y^{2} + 3$

Step 1

Move all the expressions to the left side of the equation.

Tap for more steps...

Step 1.1

Subtract $5 y^{2}$ from both sides of the equation.

$8 y - 5 y^{2} = 3$

Step 1.2

Subtract $3$ from both sides of the equation.

$8 y - 5 y^{2} - 3 = 0$

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 $a = - 5$ , $b = 8$ , and $c = - 3$ into the quadratic formula and solve for $y$ .

$\frac{- 8 \pm \sqrt{8^{2} - 4 \cdot (- 5 \cdot - 3)}}{2 \cdot - 5}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Raise $8$ to the power of $2$ .

$y = \frac{- 8 \pm \sqrt{64 - 4 \cdot - 5 \cdot - 3}}{2 \cdot - 5}$

Step 4.1.2

Multiply $- 4 \cdot - 5 \cdot - 3$ .

Tap for more steps...

Step 4.1.2.1

Multiply $- 4$ by $- 5$ .

$y = \frac{- 8 \pm \sqrt{64 + 20 \cdot - 3}}{2 \cdot - 5}$

Step 4.1.2.2

Multiply $20$ by $- 3$ .

$y = \frac{- 8 \pm \sqrt{64 - 60}}{2 \cdot - 5}$

Step 4.1.3

Subtract $60$ from $64$ .

$y = \frac{- 8 \pm \sqrt{4}}{2 \cdot - 5}$

Step 4.1.4

Rewrite $4$ as $2^{2}$ .

$y = \frac{- 8 \pm \sqrt{2^{2}}}{2 \cdot - 5}$

Step 4.1.5

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

$y = \frac{- 8 \pm 2}{2 \cdot - 5}$

Step 4.2

Multiply $2$ by $- 5$ .

$y = \frac{- 8 \pm 2}{- 10}$

Step 4.3

Simplify $\frac{- 8 \pm 2}{- 10}$ .

$y = \frac{4 \pm 1}{5}$

Step 5

The final answer is the combination of both solutions.

$y = 1, \frac{3}{5}$