Solve Using the Quadratic Formula 0.6x^2=2.4x+0.6

$0.6 x^{2} = 2.4 x + 0.6$

Step 1

Move all the expressions to the left side of the equation.

Subtract $2.4 x$ from both sides of the equation.

$0.6 x^{2} - 2.4 x = 0.6$

Subtract $0.6$ from both sides of the equation.

$0.6 x^{2} - 2.4 x - 0.6 = 0$

Step 2

Use the quadratic formula to find the solutions.

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

Step 3

Substitute the values $a = 0.6$ , $b = - 2.4$ , and $c = - 0.6$ into the quadratic formula and solve for $x$ .

$\frac{2.4 \pm \sqrt{{(- 2.4)}^{2} - 4 \cdot (0.6 \cdot - 0.6)}}{2 \cdot 0.6}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 2.4$ to the power of $2$ .

$x = \frac{2.4 \pm \sqrt{5.76 - 4 \cdot 0.6 \cdot - 0.6}}{2 \cdot 0.6}$

Multiply $- 4 \cdot 0.6 \cdot - 0.6$ .

Multiply $- 4$ by $0.6$ .

$x = \frac{2.4 \pm \sqrt{5.76 - 2.4 \cdot - 0.6}}{2 \cdot 0.6}$

Multiply $- 2.4$ by $- 0.6$ .

$x = \frac{2.4 \pm \sqrt{5.76 + 1.44}}{2 \cdot 0.6}$

Add $5.76$ and $1.44$ .

$x = \frac{2.4 \pm \sqrt{7.2}}{2 \cdot 0.6}$

Multiply $2$ by $0.6$ .

$x = \frac{2.4 \pm \sqrt{7.2}}{1.2}$

Simplify $\frac{2.4 \pm \sqrt{7.2}}{1.2}$ .

$x = \frac{12 \pm 5 \sqrt{7.2}}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{12 \pm 5 \sqrt{7.2}}{6}$

Decimal Form:

$x = 4.23606797 \dots, - 0.23606797 \dots$