How do you solve $3 x^{2} = - 4 x + 2$ $3x^2=- 4x+2$ ?

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How do you solve $3 x^{2} = - 4 x + 2$ $3x^2=- 4x+2$ ?

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Answer 1 · 2015-05-16T13:05:34

$3 x^{2} = - 4 x + 2$ $3x^2=-4x+2$
can be re-arranged as
$3 x^{2} + 4 x - 2 = 0$ $3x^2+4x-2 = 0$

which has the general form
$a x^{2} + b x + c = 0$ $ax^2+bx+c = 0$
with solutions given by the quadratic formula
$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $x= (-b+-sqrt(b^2-4ac))/(2a)$

In this case
$x = \frac{- 4 \pm \sqrt{4^{2} - 4 (3) (- 2)}}{2 (3)}$ $x= (-4 +-sqrt(4^2- 4(3)(-2)))/(2(3))$

$x = \frac{- 2 \pm \sqrt{10}}{3}$ $x= (-2+-sqrt(10))/3$

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How do you solve $3 x^{2} = - 4 x + 2$ $3x^2=- 4x+2$ ?

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