Solve 92 = (1 - (15.6 - 12.6)/(0.14 x (x - 806))) x 100.

Step-by-step solution

1. 1

   Simplify the innermost numerator. $15.6-12.6 = 3$, so the equation becomes $92 = \left(1-\frac{3}{0.14(x-806)}\right)\cdot 100.$ Always collapse constants before unwrapping the structure.

2. 2

   Undo the outermost operation. The bracket is multiplied by $100$, so divide both sides by $100$: $0.92 = 1-\frac{3}{0.14(x-806)}.$ Reading the equation as a percentage: the fraction accounts for the $8\%$ shortfall from $100\%$.

3. 3

   Isolate the fraction. Subtract $1$: $-0.08 = -\dfrac{3}{0.14(x-806)}$, and multiplying by $-1$ gives $0.08 = \frac{3}{0.14(x-806)}.$

4. 4

   Clear the denominator. Multiplying both sides by $0.14(x-806)$ and using $0.08\cdot0.14 = 0.0112$: $0.0112\,(x-806) = 3.$

5. 5

   Solve for the bracket, then for x. $x-806 = \frac{3}{0.0112} = \frac{1875}{7} = 267.\overline{857142},$ so $x = 806+\frac{1875}{7} = \frac{7517}{7} \approx 1073.86.$ Converting $0.0112$ to the fraction $\tfrac{112}{10000} = \tfrac{7}{625}$ makes the exact value visible: $\tfrac{3\cdot625}{7} = \tfrac{1875}{7}$.

6. 6

   Verify by substitution. With $x-806 = \tfrac{1875}{7}$, $0.14(x-806) = \tfrac{7}{50}\cdot\tfrac{1875}{7} = 37.5$, and $\tfrac{3}{37.5} = 0.08$; then $(1-0.08)\cdot100 = 92$ exactly, as required.