# How do you solve using the quadratic formula 4x-3x^2=1?

May 9, 2015

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
is applicable to equations in the form:
$a {x}^{2} + b x + c = 0$

So first it will be necessary to rearrange $4 x - 3 {x}^{2} = 1$ as
$3 {x}^{2} - 4 x + 1 = 0$

Then
$x = \frac{4 \pm \sqrt{{4}^{2} - 4 \left(3\right) \left(1\right)}}{2 \left(3\right)}$

$= \frac{4 \pm 2}{6}$

$x = 1$ or $x = \frac{1}{3}$