Solve for \( x \) without the use of a calculator: \( 2.1 .2 P=\frac{3}{2} x\left(P Q^{2}-P q^{2}\right) \)

To solve for \( x \) in the equation \( 2.1 .2 P=\frac{3}{2} x\left(P Q^{2}-P q^{2}\right) \), we can follow these steps: 1. First, simplify the terms on the right side: - Factor out \( P \) from \( P Q^{2} - P q^{2} \): \[ P (Q^{2} - q^{2}) \] Thus, the equation can be rewritten as: \[ 2.1 .2 P = \frac{3}{2} x P (Q^{2} - q^{2}) \] 2. Next, divide both sides by \( P \) (assuming \( P \neq 0 \)): \[ 2.1 .2 = \frac{3}{2} x (Q^{2} - q^{2}) \] 3. Now isolate \( x \) by multiplying both sides by \( \frac{2}{3(Q^{2} - q^{2})} \): \[ x = \frac{2 \cdot 2.1 .2}{3(Q^{2} - q^{2})} \] 4. Now compute \( 2.1 .2 \): \[ 2.1 \cdot 2 = 4.2 \] \[ 4.2 \cdot 0.2 = 0.84 \] Therefore: \[ x = \frac{2 \cdot 0.84}{3(Q^{2} - q^{2})} \] Simplifying gives: \[ x = \frac{1.68}{3(Q^{2} - q^{2})} \] 5. Finally: \[ x = \frac{0.56}{Q^{2} - q^{2}} \] So the solution for \( x \) is: \[ x = \frac{0.56}{Q^{2} - q^{2}} \]