Solve Using the Quadratic Formula 5v^2-21=10v

$5 v^{2} - 21 = 10 v$

Step 1

Subtract $10 v$ from both sides of the equation.

$5 v^{2} - 21 - 10 v = 0$

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 $a = 5$ , $b = - 10$ , and $c = - 21$ into the quadratic formula and solve for $v$ .

$\frac{10 \pm \sqrt{{(- 10)}^{2} - 4 \cdot (5 \cdot - 21)}}{2 \cdot 5}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 10$ to the power of $2$ .

$v = \frac{10 \pm \sqrt{100 - 4 \cdot 5 \cdot - 21}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot - 21$ .

Multiply $- 4$ by $5$ .

$v = \frac{10 \pm \sqrt{100 - 20 \cdot - 21}}{2 \cdot 5}$

Multiply $- 20$ by $- 21$ .

$v = \frac{10 \pm \sqrt{100 + 420}}{2 \cdot 5}$

Add $100$ and $420$ .

$v = \frac{10 \pm \sqrt{520}}{2 \cdot 5}$

Rewrite $520$ as $2^{2} \cdot 130$ .

Factor $4$ out of $520$ .

$v = \frac{10 \pm \sqrt{4 (130)}}{2 \cdot 5}$

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

$v = \frac{10 \pm \sqrt{2^{2} \cdot 130}}{2 \cdot 5}$

Pull terms out from under the radical.

$v = \frac{10 \pm 2 \sqrt{130}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$v = \frac{10 \pm 2 \sqrt{130}}{10}$

Simplify $\frac{10 \pm 2 \sqrt{130}}{10}$ .

$v = \frac{5 \pm \sqrt{130}}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$v = \frac{5 \pm \sqrt{130}}{5}$

Decimal Form:

$v = 3.28035085 \dots, - 1.28035085 \dots$