Find All Complex Solutions -1.5x^2+4x+2.2=0

$- 1.5 x^{2} + 4 x + 2.2 = 0$

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 $a = - 1.5$ , $b = 4$ , and $c = 2.2$ into the quadratic formula and solve for $x$ .

$\frac{- 4 \pm \sqrt{4^{2} - 4 \cdot (- 1.5 \cdot 2.2)}}{2 \cdot - 1.5}$

Step 3

Simplify.

Simplify the numerator.

Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot - 1.5 \cdot 2.2}}{2 \cdot - 1.5}$

Multiply $- 4 \cdot - 1.5 \cdot 2.2$ .

Multiply $- 4$ by $- 1.5$ .

$x = \frac{- 4 \pm \sqrt{16 + 6 \cdot 2.2}}{2 \cdot - 1.5}$

Multiply $6$ by $2.2$ .

$x = \frac{- 4 \pm \sqrt{16 + 13.2}}{2 \cdot - 1.5}$

Add $16$ and $13.2$ .

$x = \frac{- 4 \pm \sqrt{29.2}}{2 \cdot - 1.5}$

Multiply $2$ by $- 1.5$ .

$x = \frac{- 4 \pm \sqrt{29.2}}{- 3}$

Simplify $\frac{- 4 \pm \sqrt{29.2}}{- 3}$ .

$x = \frac{4 \pm \sqrt{29.2}}{3}$

Multiply by $1$ .

$x = \frac{1 (4 \pm \sqrt{29.2})}{3}$

Factor $3$ out of $3$ .

$x = \frac{1 (4 \pm \sqrt{29.2})}{3 (1)}$

Separate fractions.

$x = \frac{1}{3} \cdot \frac{4 \pm \sqrt{29.2}}{1}$

Divide $1$ by $3$ .

$x = 0.\overline{3} (\frac{4 \pm \sqrt{29.2}}{1})$

Divide $4 \pm \sqrt{29.2}$ by $1$ .

$x = 0.\overline{3} (4 \pm \sqrt{29.2})$

Step 4

The final answer is the combination of both solutions.

$x = 3.13456747, - 0.46790081$