Find the Roots (Zeros) 3x^2+15x-21=0

$3 x^{2} + 15 x - 21 = 0$

Factor $3$ out of $3 x^{2} + 15 x - 21$ .

Factor $3$ out of $3 x^{2}$ .

$3 (x^{2}) + 15 x - 21 = 0$

Factor $3$ out of $15 x$ .

$3 (x^{2}) + 3 (5 x) - 21 = 0$

Factor $3$ out of $- 21$ .

$3 x^{2} + 3 (5 x) + 3 \cdot - 7 = 0$

Factor $3$ out of $3 x^{2} + 3 (5 x)$ .

$3 (x^{2} + 5 x) + 3 \cdot - 7 = 0$

Factor $3$ out of $3 (x^{2} + 5 x) + 3 \cdot - 7$ .

$3 (x^{2} + 5 x - 7) = 0$

Divide each term in $3 (x^{2} + 5 x - 7) = 0$ by $3$ and simplify.

Divide each term in $3 (x^{2} + 5 x - 7) = 0$ by $3$ .

$\frac{3 (x^{2} + 5 x - 7)}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (x^{2} + 5 x - 7)}{3} = \frac{0}{3}$

Divide $x^{2} + 5 x - 7$ by $1$ .

$x^{2} + 5 x - 7 = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

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

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 1$ , $b = 5$ , and $c = - 7$ into the quadratic formula and solve for $x$ .

$\frac{- 5 \pm \sqrt{5^{2} - 4 \cdot (1 \cdot - 7)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $5$ to the power of $2$ .

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot 1 \cdot - 7}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{- 5 \pm \sqrt{25 - 4 \cdot - 7}}{2 \cdot 1}$

Multiply $- 4$ by $- 7$ .

$x = \frac{- 5 \pm \sqrt{25 + 28}}{2 \cdot 1}$

Add $25$ and $28$ .

$x = \frac{- 5 \pm \sqrt{53}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 5 \pm \sqrt{53}}{2}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 5 \pm \sqrt{53}}{2}$

Decimal Form:

$x = 1.14005494 \dots, - 6.14005494 \dots$