Solve x-53x^2=6x-23

Evaluate

x - 53 x^{2} = 6 x - 23

Move the expression to the left side

- 5 x - 53 x^{2} + 23 = 0

Rewrite in standard form

- 53 x^{2} - 5 x + 23 = 0

Multiply both sides

53 x^{2} + 5 x - 23 = 0

Substitute a= 53,b= 5 and c= - 23 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 5 \pm 5 ^{2} - 4 \times 53 ( - 23 )}{2 \times 53}

Simplify the expression

x = \frac{- 5 \pm 5 ^{2} - 4 \times 53 ( - 23 )}{106}

Simplify the expression

More Steps

x = \frac{- 5 \pm 4901}{106}

Simplify the radical expression

More Steps

x = \frac{- 5 \pm 13 29}{106}

Separate the equation into 2 possible cases

x = \frac{- 5 + 13 29}{106} x = \frac{- 5 - 13 29}{106}

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

x = \frac{- 5 + 13 29}{106} x = - \frac{5 + 13 29}{106}

Solution

x_{1} = - \frac{5 + 13 29}{106}, x_{2} = \frac{- 5 + 13 29}{106}

Alternative Form

x_{1} \approx - 0.707615, x_{2} \approx 0.613275

Solve the quadratic equation