# How do you solve 2x^2=6x-2 using the quadratic formula?

Feb 20, 2016

$x = \frac{3 + \sqrt{5}}{2}$ or $\frac{3 - \sqrt{5}}{2}$

#### Explanation:

Using quadratic formula, solution of the equation $a {x}^{2} + b x + c = 0$ is given by $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$. Note that the quadratic equation is in its general form.

Hence converting the equation to its general form, the equation 2x^2=6x−2 this becomes $2 {x}^{2} - 6 x + 2 = 0$ or dividing by $2$, ${x}^{2} - 3 x + 1 = 0$ and as such $a = 1 , b = - 3$ and $c = 1$.

Hence, solution is given by $x = \frac{- \left(- 3\right) \pm \sqrt{{\left(- 3\right)}^{2} - 4 \cdot 1 \cdot 1}}{2 \cdot 1}$ or

$x = \frac{3 \pm \sqrt{9 - 4}}{2}$ or $x = \frac{3 \pm \sqrt{5}}{2}$ i.e.

$x = \frac{3 + \sqrt{5}}{2}$ or $\frac{3 - \sqrt{5}}{2}$