Solve Using the Quadratic Formula 2x^2=3-4x

$2 x^{2} = 3 - 4 x$

Step 1

Move all the expressions to the left side of the equation.

Subtract $3$ from both sides of the equation.

$2 x^{2} - 3 = - 4 x$

Add $4 x$ to both sides of the equation.

$2 x^{2} - 3 + 4 x = 0$

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 $a = 2$ , $b = 4$ , and $c = - 3$ into the quadratic formula and solve for $x$ .

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

Step 4

Simplify.

Simplify the numerator.

Raise $4$ to the power of $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 4 \cdot 2 \cdot - 3}}{2 \cdot 2}$

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

Multiply $- 4$ by $2$ .

$x = \frac{- 4 \pm \sqrt{16 - 8 \cdot - 3}}{2 \cdot 2}$

Multiply $- 8$ by $- 3$ .

$x = \frac{- 4 \pm \sqrt{16 + 24}}{2 \cdot 2}$

Add $16$ and $24$ .

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

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$x = \frac{- 4 \pm \sqrt{4 (10)}}{2 \cdot 2}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 4 \pm \sqrt{2^{2} \cdot 10}}{2 \cdot 2}$

Pull terms out from under the radical.

$x = \frac{- 4 \pm 2 \sqrt{10}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 4 \pm 2 \sqrt{10}}{4}$

Simplify $\frac{- 4 \pm 2 \sqrt{10}}{4}$ .

$x = \frac{- 2 \pm \sqrt{10}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 2 \pm \sqrt{10}}{2}$

Decimal Form:

$x = 0.58113883 \dots, - 2.58113883 \dots$