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

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

Step 1

Subtract $3$ from both sides of the equation.

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

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

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

Step 4

Simplify.

Simplify the numerator.

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

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

Multiply $- 4 \cdot 6 \cdot - 3$ .

Multiply $- 4$ by $6$ .

$x = \frac{4 \pm \sqrt{16 - 24 \cdot - 3}}{2 \cdot 6}$

Multiply $- 24$ by $- 3$ .

$x = \frac{4 \pm \sqrt{16 + 72}}{2 \cdot 6}$

Add $16$ and $72$ .

$x = \frac{4 \pm \sqrt{88}}{2 \cdot 6}$

Rewrite $88$ as $2^{2} \cdot 22$ .

Factor $4$ out of $88$ .

$x = \frac{4 \pm \sqrt{4 (22)}}{2 \cdot 6}$

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

$x = \frac{4 \pm \sqrt{2^{2} \cdot 22}}{2 \cdot 6}$

Pull terms out from under the radical.

$x = \frac{4 \pm 2 \sqrt{22}}{2 \cdot 6}$

Multiply $2$ by $6$ .

$x = \frac{4 \pm 2 \sqrt{22}}{12}$

Simplify $\frac{4 \pm 2 \sqrt{22}}{12}$ .

$x = \frac{2 \pm \sqrt{22}}{6}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2 \pm \sqrt{22}}{6}$

Decimal Form:

$x = 1.11506929 \dots, - 0.44840262 \dots$