# How do you solve the quadratic using the quadratic formula given 3a^2=6a-3?

Jan 17, 2017

$a = 1$

#### Explanation:

Rearrange:
$3 {a}^{2} - 6 a + 3 = 0$

Use the formula $a = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$ taking care not to get the $a$'s muddled

Formula Problem
a 3
b -6
c 3
x a

$a = \frac{- \left(- 6\right) \pm \sqrt{{\left(- 6\right)}^{2} - 4 \times 3 \times 3}}{2 \times 3}$
$a = \frac{6 \pm 0}{2 \times 3}$
$a = 1$ (repeated root).

Check: $3 \times {\left(1\right)}^{2} = 3$ and $6 \times \left(1\right) - 3 = 3$

If you get muddled over the $a$'s just replace all the $a$'s with $x$'s, apply the formula, then at the step replace the $x$ with $a$.