Solve Using the Quadratic Formula 8x^2-24=3x^2-9

$8 x^{2} - 24 = 3 x^{2} - 9$

Step 1

Move all terms to the left side of the equation and simplify.

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

Subtract $3 x^{2}$ from both sides of the equation.

$8 x^{2} - 24 - 3 x^{2} = - 9$

Add $9$ to both sides of the equation.

$8 x^{2} - 24 - 3 x^{2} + 9 = 0$

Simplify $8 x^{2} - 24 - 3 x^{2} + 9$ .

Subtract $3 x^{2}$ from $8 x^{2}$ .

$5 x^{2} - 24 + 9 = 0$

Add $- 24$ and $9$ .

$5 x^{2} - 15 = 0$

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 $a = 5$ , $b = 0$ , and $c = - 15$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (5 \cdot - 15)}}{2 \cdot 5}$

Step 4

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 5 \cdot - 15}}{2 \cdot 5}$

Multiply $- 4 \cdot 5 \cdot - 15$ .

Multiply $- 4$ by $5$ .

$x = \frac{0 \pm \sqrt{0 - 20 \cdot - 15}}{2 \cdot 5}$

Multiply $- 20$ by $- 15$ .

$x = \frac{0 \pm \sqrt{0 + 300}}{2 \cdot 5}$

Add $0$ and $300$ .

$x = \frac{0 \pm \sqrt{300}}{2 \cdot 5}$

Rewrite $300$ as $10^{2} \cdot 3$ .

Factor $100$ out of $300$ .

$x = \frac{0 \pm \sqrt{100 (3)}}{2 \cdot 5}$

Rewrite $100$ as $10^{2}$ .

$x = \frac{0 \pm \sqrt{10^{2} \cdot 3}}{2 \cdot 5}$

Pull terms out from under the radical.

$x = \frac{0 \pm 10 \sqrt{3}}{2 \cdot 5}$

Multiply $2$ by $5$ .

$x = \frac{0 \pm 10 \sqrt{3}}{10}$

Simplify $\frac{0 \pm 10 \sqrt{3}}{10}$ .

$x = \pm \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{3}$

Decimal Form:

$x = 1.73205080 \dots, - 1.73205080 \dots$

Solve Using the Quadratic Formula 8x^2-24=3x^2-9

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