Solve 3x (60-x) 80 = 180

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{60 - 3597}{2}, x_{2} = \frac{60 + 3597}{2}

Alternative Form

x_{1} \approx 0.012503, x_{2} \approx 59.987497

Evaluate

3 x (60 - x) \times 80 = 180

Multiply the terms

240 x (60 - x) = 180

Expand the expression

More Steps

14400 x - 240 x^{2} = 180

Move the expression to the left side

14400 x - 240 x^{2} - 180 = 0

Rewrite in standard form

- 240 x^{2} + 14400 x - 180 = 0

Multiply both sides

240 x^{2} - 14400 x + 180 = 0

Substitute a= 240,b= - 14400 and c= 180 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{14400 \pm ( - 14400 ) ^{2} - 4 \times 240 \times 180}{2 \times 240}

Simplify the expression

x = \frac{14400 \pm ( - 14400 ) ^{2} - 4 \times 240 \times 180}{480}

Simplify the expression

More Steps

x = \frac{14400 \pm 1440 0 ^{2} - 172800}{480}

Simplify the radical expression

More Steps

x = \frac{14400 \pm 240 3597}{480}

Separate the equation into 2 possible cases

x = \frac{14400 + 240 3597}{480} x = \frac{14400 - 240 3597}{480}

Simplify the expression

More Steps

x = \frac{60 + 3597}{2} x = \frac{14400 - 240 3597}{480}

Simplify the expression

More Steps

x = \frac{60 + 3597}{2} x = \frac{60 - 3597}{2}

Solution

x_{1} = \frac{60 - 3597}{2}, x_{2} = \frac{60 + 3597}{2}

Alternative Form

x_{1} \approx 0.012503, x_{2} \approx 59.987497

Show Solution