Solve Using the Quadratic Formula -2x^2+7x-4=0

$- 2 x^{2} + 7 x - 4 = 0$

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 $a = - 2$ , $b = 7$ , and $c = - 4$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (- 2 \cdot - 4)}}{2 \cdot - 2}$

Step 3

Simplify.

Simplify the numerator.

Raise $7$ to the power of $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot - 2 \cdot - 4}}{2 \cdot - 2}$

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

Multiply $- 4$ by $- 2$ .

$x = \frac{- 7 \pm \sqrt{49 + 8 \cdot - 4}}{2 \cdot - 2}$

Multiply $8$ by $- 4$ .

$x = \frac{- 7 \pm \sqrt{49 - 32}}{2 \cdot - 2}$

Subtract $32$ from $49$ .

$x = \frac{- 7 \pm \sqrt{17}}{2 \cdot - 2}$

Multiply $2$ by $- 2$ .

$x = \frac{- 7 \pm \sqrt{17}}{- 4}$

Simplify $\frac{- 7 \pm \sqrt{17}}{- 4}$ .

$x = \frac{7 \pm \sqrt{17}}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7 \pm \sqrt{17}}{4}$

Decimal Form:

$x = 2.78077640 \dots, 0.71922359 \dots$