Solve 123(x-3)=60-(x^2)

Evaluate

123 (x - 3) = 60 - x^{2}

Swap the sides

60 - x^{2} = 123 (x - 3)

Expand the expression

More Steps

60 - x^{2} = 123 x - 369

Move the expression to the left side

429 - x^{2} - 123 x = 0

Rewrite in standard form

- x^{2} - 123 x + 429 = 0

Multiply both sides

x^{2} + 123 x - 429 = 0

Substitute a= 1,b= 123 and c= - 429 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 123 \pm 12 3 ^{2} - 4 ( - 429 )}{2}

Simplify the expression

More Steps

x = \frac{- 123 \pm 16845}{2}

Separate the equation into 2 possible cases

x = \frac{- 123 + 16845}{2} x = \frac{- 123 - 16845}{2}

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

x = \frac{- 123 + 16845}{2} x = - \frac{123 + 16845}{2}

Solution

x_{1} = - \frac{123 + 16845}{2}, x_{2} = \frac{- 123 + 16845}{2}

Alternative Form

x_{1} \approx - 126.394145, x_{2} \approx 3.394145

Solve the quadratic equation