Solve Using the Quadratic Formula 2x^2-5x-3=0

$2 x^{2} - 5 x - 3 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 2$ , $b = - 5$ , and $c = - 3$ into the quadratic formula and solve for $x$ .

$\frac{5 \pm \sqrt{{(- 5)}^{2} - 4 \cdot (2 \cdot - 3)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

Raise $- 5$ to the power of $2$ .

$x = \frac{5 \pm \sqrt{25 - 4 \cdot 2 \cdot - 3}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 3$ .

Multiply $- 4$ by $2$ .

$x = \frac{5 \pm \sqrt{25 - 8 \cdot - 3}}{2 \cdot 2}$

Multiply $- 8$ by $- 3$ .

$x = \frac{5 \pm \sqrt{25 + 24}}{2 \cdot 2}$

Add $25$ and $24$ .

$x = \frac{5 \pm \sqrt{49}}{2 \cdot 2}$

Rewrite $49$ as $7^{2}$ .

$x = \frac{5 \pm \sqrt{7^{2}}}{2 \cdot 2}$

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

$x = \frac{5 \pm 7}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{5 \pm 7}{4}$

Step 4

The final answer is the combination of both solutions.

$x = 3, - \frac{1}{2}$