# What is the quadratic equation of 3x^2 + 6x = 12?

Oct 25, 2015

In standard form you might write it $3 {x}^{2} + 6 x - 12 = 0$

#### Explanation:

Standard form for a quadratic equation in one variable $x$ is:

$a {x}^{2} + b x + c = 0$

In our case, we can get our equation into standard form by subtracting $12$ from both sides to get:

$3 {x}^{2} + 6 x - 12 = 0$

In addition, all of the coefficients are divisible by $3$, so we can divide through by $3$ to get the equivalent equation:

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

...which is in standard form with $a = 1$, $b = 2$ and $c = - 4$.

Then we can use the quadratic formula to find the solutions:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a} = \frac{2 \pm \sqrt{{2}^{2} - \left(4 \times 1 \times - 4\right)}}{2 \cdot 1} = \frac{2 \pm \sqrt{4 + 16}}{2}$

$= \frac{2 \pm \sqrt{20}}{2} = \frac{2 \pm \sqrt{{2}^{2} \cdot 5}}{2} = \frac{2 \pm \sqrt{{2}^{2}} \sqrt{5}}{2} = \frac{2 \pm 2 \sqrt{5}}{2}$

$= 1 \pm \sqrt{5}$