Solve thr proprtion for x. 14/20=17/x+12

Solve thr proprtion for x. 14/20=17/x+12cross multiply:
14 * x + 12 = 20 * 17
Simplifying14 * x + 12 = 20 * 17
Reorder the terms:14 * 12 + x = 20 * 1712 * 14 + x * 14 = 20 * 17168 + 14x = 20 * 17
Multiply 20 * 17168 + 14x = 340
Solving168 + 14x = 340
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-168' to each side of the equation.168 + -168 + 14x = 340 + -168
Combine like terms: 168 + -168 = 00 + 14x = 340 + -16814x = 340 + -168
Combine like terms: 340 + -168 = 17214x = 172
Divide each side by '14'.x = 12.28571429
Simplifyingx = 12.28571429

I must assume that you meant 14/20 = 17 / (x+12).  If so, it's important to use parentheses to indicate that you are dividing 17 by (x+12).

Then your equation of proportions (ratios) is

  14              17
=
20              x+12

Let's cross-multiply:  14(x+12) = 340

Divide both sides by 14 to isolate (x+12):  x+12 = 340/14 = 24.29

Subtracting 12 from both sides, we get x = 12.29

You should check this answer by subst. it into the original equation of ratios.