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

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

Step 1

Subtract $24$ from both sides of the equation.

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

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

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

Step 4

Simplify.

Simplify the numerator.

Raise $3$ to the power of $2$ .

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot 1 \cdot - 24}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 24$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 3 \pm \sqrt{9 - 4 \cdot - 24}}{2 \cdot 1}$

Multiply $- 4$ by $- 24$ .

$x = \frac{- 3 \pm \sqrt{9 + 96}}{2 \cdot 1}$

Add $9$ and $96$ .

$x = \frac{- 3 \pm \sqrt{105}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 3 \pm \sqrt{105}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 3 \pm \sqrt{105}}{2}$

Decimal Form:

$x = 3.62347538 \dots, - 6.62347538 \dots$