Basic Math Examples

$- 5 y^{2} - 3 y - 4 y = - 2$

Step 1

Subtract $4 y$ from $- 3 y$ .

$- 5 y^{2} - 7 y = - 2$

Step 2

Add $2$ to both sides of the equation.

$- 5 y^{2} - 7 y + 2 = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = - 5$ , $b = - 7$ , and $c = 2$ into the quadratic formula and solve for $y$ .

$\frac{7 \pm \sqrt{{(- 7)}^{2} - 4 \cdot (- 5 \cdot 2)}}{2 \cdot - 5}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

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

$y = \frac{7 \pm \sqrt{49 - 4 \cdot - 5 \cdot 2}}{2 \cdot - 5}$

Step 5.1.2

Multiply $- 4 \cdot - 5 \cdot 2$ .

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Step 5.1.2.1

Multiply $- 4$ by $- 5$ .

$y = \frac{7 \pm \sqrt{49 + 20 \cdot 2}}{2 \cdot - 5}$

Step 5.1.2.2

Multiply $20$ by $2$ .

$y = \frac{7 \pm \sqrt{49 + 40}}{2 \cdot - 5}$

Step 5.1.3

Add $49$ and $40$ .

$y = \frac{7 \pm \sqrt{89}}{2 \cdot - 5}$

Step 5.2

Multiply $2$ by $- 5$ .

$y = \frac{7 \pm \sqrt{89}}{- 10}$

Step 5.3

Move the negative in front of the fraction.

$y = - \frac{7 \pm \sqrt{89}}{10}$

Step 6

The final answer is the combination of both solutions.

$y = - \frac{7 + \sqrt{89}}{10}, - \frac{7 - \sqrt{89}}{10}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{7 + \sqrt{89}}{10}, - \frac{7 - \sqrt{89}}{10}$

Decimal Form:

$y = - 1.64339811 \dots, 0.24339811 \dots$