Solve x (x-366)/5-15=1500

Question

Solve the equation

x_{1} = 183 - 210266, x_{2} = 183 + 210266

Alternative Form

x_{1} \approx - 19.642542, x_{2} \approx 385.642542

Evaluate

x \times \frac{x - 366}{5} - 15 = 1500

Multiply the terms

\frac{x ( x - 366 )}{5} - 15 = 1500

Multiply both sides of the equation by LCD

(\frac{x ( x - 366 )}{5} - 15) \times 5 = 1500 \times 5

Simplify the equation

More Steps

x^{2} - 366 x - 75 = 1500 \times 5

Simplify the equation

x^{2} - 366 x - 75 = 7500

Move the expression to the left side

x^{2} - 366 x - 75 - 7500 = 0

Subtract the numbers

x^{2} - 366 x - 7575 = 0

Substitute a= 1,b= - 366 and c= - 7575 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{366 \pm ( - 366 ) ^{2} - 4 ( - 7575 )}{2}

Simplify the expression

More Steps

x = \frac{366 \pm 36 6 ^{2} + 30300}{2}

Simplify the radical expression

More Steps

x = \frac{366 \pm 4 10266}{2}

Separate the equation into 2 possible cases

x = \frac{366 + 4 10266}{2} x = \frac{366 - 4 10266}{2}

Simplify the expression

More Steps

x = 183 + 210266 x = \frac{366 - 4 10266}{2}

Simplify the expression

More Steps

x = 183 + 210266 x = 183 - 210266

Solution

x_{1} = 183 - 210266, x_{2} = 183 + 210266

Alternative Form

x_{1} \approx - 19.642542, x_{2} \approx 385.642542

Show Solution