Solve x = 15 - 3x^2

Evaluate

x = 15 - 3 x^{2}

Swap the sides

15 - 3 x^{2} = x

Move the expression to the left side

15 - 3 x^{2} - x = 0

Rewrite in standard form

- 3 x^{2} - x + 15 = 0

Multiply both sides

3 x^{2} + x - 15 = 0

Substitute a= 3,b= 1 and c= - 15 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 1 \pm 1 ^{2} - 4 \times 3 ( - 15 )}{2 \times 3}

Simplify the expression

x = \frac{- 1 \pm 1 ^{2} - 4 \times 3 ( - 15 )}{6}

Simplify the expression

More Steps

x = \frac{- 1 \pm 181}{6}

Separate the equation into 2 possible cases

x = \frac{- 1 + 181}{6} x = \frac{- 1 - 181}{6}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = \frac{- 1 + 181}{6} x = - \frac{1 + 181}{6}

Solution

x_{1} = - \frac{1 + 181}{6}, x_{2} = \frac{- 1 + 181}{6}

Alternative Form

x_{1} \approx - 2.408937, x_{2} \approx 2.075604

Solve the quadratic equation