Isolate the term with .

$$2 \times \Delta = 37 - 13$$ $$2 \times \Delta = 24$$

$$\Delta = \frac{24}{2}$$ $$\Delta = 12$$

Using the train and improvement method:

problem solution ($\Delta$)	test	conclusion
10	$2 \times 10 + 13 = 20 + 13 = 33$	$33 < 37$, too low
15	$2 \times 15 + 13 = 30 + 13 = 43$	$43 > 37$, too high
12	$2 \times 12 + 13 = 24 + 13 = 37$	$37 = 37$, correct

The solution is $\boxed{\Delta = 12}$.

$$14 \times \Delta = 77 + 21$$ $$14 \times \Delta = 98$$

$$\Delta = \frac{98}{14}$$ $$\Delta = 7$$

Using the train and improvement method:

problem solution ($\Delta$)	test	conclusion
5	$14 \times 5 - 21 = 70 - 21 = 49$	$49 < 77$, too low
10	$14 \times 10 - 21 = 140 - 21 = 119$	$119 > 77$, too high
7	$14 \times 7 - 21 = 98 - 21 = 77$	$77 = 77$, correct

The solution is $\boxed{\Delta = 7}$.