Solve Using the Quadratic Formula x+3=24x^2

$x + 3 = 24 x^{2}$

Step 1

Subtract $24 x^{2}$ from both sides of the equation.

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

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 $a = - 24$ , $b = 1$ , and $c = 3$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (- 24 \cdot 3)}}{2 \cdot - 24}$

Step 4

Simplify.

Simplify the numerator.

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot - 24 \cdot 3}}{2 \cdot - 24}$

Multiply $- 4 \cdot - 24 \cdot 3$ .

Multiply $- 4$ by $- 24$ .

$x = \frac{- 1 \pm \sqrt{1 + 96 \cdot 3}}{2 \cdot - 24}$

Multiply $96$ by $3$ .

$x = \frac{- 1 \pm \sqrt{1 + 288}}{2 \cdot - 24}$

Add $1$ and $288$ .

$x = \frac{- 1 \pm \sqrt{289}}{2 \cdot - 24}$

Rewrite $289$ as $17^{2}$ .

$x = \frac{- 1 \pm \sqrt{17^{2}}}{2 \cdot - 24}$

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

$x = \frac{- 1 \pm 17}{2 \cdot - 24}$

Multiply $2$ by $- 24$ .

$x = \frac{- 1 \pm 17}{- 48}$

Simplify $\frac{- 1 \pm 17}{- 48}$ .

$x = \frac{1 \pm 17}{48}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{3}{8}, - \frac{1}{3}$