Solve Using the Quadratic Formula 4x^2=3-6x

$4 x^{2} = 3 - 6 x$

Step 1

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

Subtract $3$ from both sides of the equation.

$4 x^{2} - 3 = - 6 x$

Add $6 x$ to both sides of the equation.

$4 x^{2} - 3 + 6 x = 0$

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 $a = 4$ , $b = 6$ , and $c = - 3$ into the quadratic formula and solve for $x$ .

$\frac{- 6 \pm \sqrt{6^{2} - 4 \cdot (4 \cdot - 3)}}{2 \cdot 4}$

Step 4

Simplify.

Simplify the numerator.

Raise $6$ to the power of $2$ .

$x = \frac{- 6 \pm \sqrt{36 - 4 \cdot 4 \cdot - 3}}{2 \cdot 4}$

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

Multiply $- 4$ by $4$ .

$x = \frac{- 6 \pm \sqrt{36 - 16 \cdot - 3}}{2 \cdot 4}$

Multiply $- 16$ by $- 3$ .

$x = \frac{- 6 \pm \sqrt{36 + 48}}{2 \cdot 4}$

Add $36$ and $48$ .

$x = \frac{- 6 \pm \sqrt{84}}{2 \cdot 4}$

Rewrite $84$ as $2^{2} \cdot 21$ .

Factor $4$ out of $84$ .

$x = \frac{- 6 \pm \sqrt{4 (21)}}{2 \cdot 4}$

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

$x = \frac{- 6 \pm \sqrt{2^{2} \cdot 21}}{2 \cdot 4}$

Pull terms out from under the radical.

$x = \frac{- 6 \pm 2 \sqrt{21}}{2 \cdot 4}$

Multiply $2$ by $4$ .

$x = \frac{- 6 \pm 2 \sqrt{21}}{8}$

Simplify $\frac{- 6 \pm 2 \sqrt{21}}{8}$ .

$x = \frac{- 3 \pm \sqrt{21}}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 3 \pm \sqrt{21}}{4}$

Decimal Form:

$x = 0.39564392 \dots, - 1.89564392 \dots$