Find All Complex Solutions 15x^2-44x+21=0

$15 x^{2} - 44 x + 21 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 15$ , $b = - 44$ , and $c = 21$ into the quadratic formula and solve for $x$ .

$\frac{44 \pm \sqrt{{(- 44)}^{2} - 4 \cdot (15 \cdot 21)}}{2 \cdot 15}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 44$ to the power of $2$ .

$x = \frac{44 \pm \sqrt{1936 - 4 \cdot 15 \cdot 21}}{2 \cdot 15}$

Multiply $- 4 \cdot 15 \cdot 21$ .

Multiply $- 4$ by $15$ .

$x = \frac{44 \pm \sqrt{1936 - 60 \cdot 21}}{2 \cdot 15}$

Multiply $- 60$ by $21$ .

$x = \frac{44 \pm \sqrt{1936 - 1260}}{2 \cdot 15}$

Subtract $1260$ from $1936$ .

$x = \frac{44 \pm \sqrt{676}}{2 \cdot 15}$

Rewrite $676$ as $26^{2}$ .

$x = \frac{44 \pm \sqrt{26^{2}}}{2 \cdot 15}$

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

$x = \frac{44 \pm 26}{2 \cdot 15}$

Multiply $2$ by $15$ .

$x = \frac{44 \pm 26}{30}$

Simplify $\frac{44 \pm 26}{30}$ .

$x = \frac{22 \pm 13}{15}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{7}{3}, \frac{3}{5}$