While solar energy powered home systems are quite expensive to install, adding some passive energy features to conventional construction can make a substantial reduction in heating and cooling costs. Passive solar requires no machinery and uses the building itself to collect, store and distribute solar energy. An excellent passive solar investment is the installation of better quality windows with high resistance to heat transmission, provided with exterior shading on the south side to cut off high angled sun rays in cooling season and let in low angled winter sun during heating season.

cost of conventional HVAC system: $11300
annual cost for HVAC in conventional house: $1290
extral installation for better Windows & shading: $2600
Annual cost for HVAC in improved house: $840
Conventional=__?__
Improved=__?__

2 answers

11300+1290n
C-conventional = 11300+1290n

C-improved = 13900+840n
(notice its not 2600 bc it asks basically for total cost over years for improved house, so thats 11300+2600= 13900)

If you want to find out when they equal the same cost, equal the two equations together

11300+1290n= 13900+840n
n= 5.8 if you round to the nearest one decimal