Solve 2000=37.5t+75^2/2

$$2000 = 37.5 t + \frac { 75 ^ { 2 } } { 2 }$$

Solve for t

$$t = -\frac{65}{3} = -21\frac{2}{3} \approx -21.666666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2.

$$4000=75t+75^{2}$$

Calculate 75 to the power of 2 and get 5625.

$$4000=75t+5625$$

Swap sides so that all variable terms are on the left hand side.

$$75t+5625=4000$$

Subtract 5625 from both sides.

$$75t=4000-5625$$

Subtract 5625 from 4000 to get -1625.

$$75t=-1625$$

Divide both sides by 75.

$$t=\frac{-1625}{75}$$

Reduce the fraction \frac{-1625}{75} to lowest terms by extracting and canceling out 25.

$$t=-\frac{65}{3}$$