Solve Using the Quadratic Formula 40x^2+2x=24

$40 x^{2} + 2 x = 24$

Step 1

Subtract $24$ from both sides of the equation.

$40 x^{2} + 2 x - 24 = 0$

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 $a = 40$ , $b = 2$ , and $c = - 24$ into the quadratic formula and solve for $x$ .

$\frac{- 2 \pm \sqrt{2^{2} - 4 \cdot (40 \cdot - 24)}}{2 \cdot 40}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{- 2 \pm \sqrt{4 - 4 \cdot 40 \cdot - 24}}{2 \cdot 40}$

Multiply $- 4 \cdot 40 \cdot - 24$ .

Multiply $- 4$ by $40$ .

$x = \frac{- 2 \pm \sqrt{4 - 160 \cdot - 24}}{2 \cdot 40}$

Multiply $- 160$ by $- 24$ .

$x = \frac{- 2 \pm \sqrt{4 + 3840}}{2 \cdot 40}$

Add $4$ and $3840$ .

$x = \frac{- 2 \pm \sqrt{3844}}{2 \cdot 40}$

Rewrite $3844$ as $62^{2}$ .

$x = \frac{- 2 \pm \sqrt{62^{2}}}{2 \cdot 40}$

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

$x = \frac{- 2 \pm 62}{2 \cdot 40}$

Multiply $2$ by $40$ .

$x = \frac{- 2 \pm 62}{80}$

Simplify $\frac{- 2 \pm 62}{80}$ .

$x = \frac{- 1 \pm 31}{40}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{3}{4}, - \frac{4}{5}$