Solve -6x=3x^2 +1

Evaluate

- 6 x = 3 x^{2} + 1

Swap the sides

3 x^{2} + 1 = - 6 x

Move the expression to the left side

3 x^{2} + 1 + 6 x = 0

Rewrite in standard form

3 x^{2} + 6 x + 1 = 0

Substitute a= 3,b= 6 and c= 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 6 \pm 6 ^{2} - 4 \times 3}{2 \times 3}

Simplify the expression

x = \frac{- 6 \pm 6 ^{2} - 4 \times 3}{6}

Simplify the expression

More Steps

x = \frac{- 6 \pm 24}{6}

Simplify the radical expression

More Steps

x = \frac{- 6 \pm 2 6}{6}

Separate the equation into 2 possible cases

x = \frac{- 6 + 2 6}{6} x = \frac{- 6 - 2 6}{6}

Simplify the expression

More Steps

x = \frac{- 3 + 6}{3} x = \frac{- 6 - 2 6}{6}

Simplify the expression

More Steps

x = \frac{- 3 + 6}{3} x = - \frac{3 + 6}{3}

Solution

x_{1} = - \frac{3 + 6}{3}, x_{2} = \frac{- 3 + 6}{3}

Alternative Form

x_{1} \approx - 1.816497, x_{2} \approx - 0.183503

Solve the quadratic equation