Solve Using the Quadratic Formula 0.3x^2-1.8x-0.3=0

$0.3 x^{2} - 1.8 x - 0.3 = 0$

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 $a = 0.3$ , $b = - 1.8$ , and $c = - 0.3$ into the quadratic formula and solve for $x$ .

$\frac{1.8 \pm \sqrt{{(- 1.8)}^{2} - 4 \cdot (0.3 \cdot - 0.3)}}{2 \cdot 0.3}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 1.8$ to the power of $2$ .

$x = \frac{1.8 \pm \sqrt{3.24 - 4 \cdot 0.3 \cdot - 0.3}}{2 \cdot 0.3}$

Multiply $- 4 \cdot 0.3 \cdot - 0.3$ .

Multiply $- 4$ by $0.3$ .

$x = \frac{1.8 \pm \sqrt{3.24 - 1.2 \cdot - 0.3}}{2 \cdot 0.3}$

Multiply $- 1.2$ by $- 0.3$ .

$x = \frac{1.8 \pm \sqrt{3.24 + 0.36}}{2 \cdot 0.3}$

Add $3.24$ and $0.36$ .

$x = \frac{1.8 \pm \sqrt{3.6}}{2 \cdot 0.3}$

Multiply $2$ by $0.3$ .

$x = \frac{1.8 \pm \sqrt{3.6}}{0.6}$

Simplify $\frac{1.8 \pm \sqrt{3.6}}{0.6}$ .

$x = \frac{9 \pm 5 \sqrt{3.6}}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{9 \pm 5 \sqrt{3.6}}{3}$

Decimal Form:

$x = 6.16227766 \dots, - 0.16227766 \dots$