To solve the equation \((654x - 10590) : 57 = 778\), follow these steps:
Multiply both sides by 57 to eliminate the division: \[ 654x - 10590 = 778 \times 57 \]
Calculate \(778 \times 57\): \[ 778 \times 57 = 44346 \] So, the equation becomes: \[ 654x - 10590 = 44346 \]
Add 10590 to both sides: \[ 654x = 44346 + 10590 \]
Calculate \(44346 + 10590\): \[ 44346 + 10590 = 54936 \] Now the equation is: \[ 654x = 54936 \]
Divide both sides by 654 to solve for \(x\): \[ x = \frac{54936}{654} \]
Calculate the division: \[ x = 84 \]
Thus, the solution is: \[ \boxed{84} \]