Find All Complex Solutions 15x^2-46x+35=0

$15 x^{2} - 46 x + 35 = 0$

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 $a = 15$ , $b = - 46$ , and $c = 35$ into the quadratic formula and solve for $x$ .

$\frac{46 \pm \sqrt{{(- 46)}^{2} - 4 \cdot (15 \cdot 35)}}{2 \cdot 15}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 46$ to the power of $2$ .

$x = \frac{46 \pm \sqrt{2116 - 4 \cdot 15 \cdot 35}}{2 \cdot 15}$

Multiply $- 4 \cdot 15 \cdot 35$ .

Multiply $- 4$ by $15$ .

$x = \frac{46 \pm \sqrt{2116 - 60 \cdot 35}}{2 \cdot 15}$

Multiply $- 60$ by $35$ .

$x = \frac{46 \pm \sqrt{2116 - 2100}}{2 \cdot 15}$

Subtract $2100$ from $2116$ .

$x = \frac{46 \pm \sqrt{16}}{2 \cdot 15}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{46 \pm \sqrt{4^{2}}}{2 \cdot 15}$

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

$x = \frac{46 \pm 4}{2 \cdot 15}$

Multiply $2$ by $15$ .

$x = \frac{46 \pm 4}{30}$

Simplify $\frac{46 \pm 4}{30}$ .

$x = \frac{23 \pm 2}{15}$

Step 4

The final answer is the combination of both solutions.

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