Question 132192
Let {{{t}}}= the original number of trucks used
{{{60/t}}} was the tons per truck 
The problems says  each truck load was reduced by 0.5 ton 
{{{60/t - .5}}} is the adjusted load per truck
Four more trucks were needed
{{{60/t - .5 = 60/(t+4)}}}
multiply both sides by {{{t(t+4)}}}
{{{60*(t+4) - .5*(t*(t+4)) = 60t}}}
{{{60t + 240 - .5*(t^2 + 4t) = 60t}}}
subtract {{{60t}}} from both sides
{{{240 - .5t^2 - 2t = 0}}}
{{{.5t^2 + 2t - 240 = 0}}}
multiply both sides by {{{2}}}
{{{t^2 + 4t - 480 = 0}}}
solve by completing the square
{{{t^2 + 4t + (4/2)^2 = 480 + (4/2)^2}}}
{{{(t + 2)^2 = 484}}}
{{{t + 2 = 22}}}
{{{t = 20}}}
Twenty trucks were required originally
check answer:
{{{60/t - .5 = 60/(t+4)}}}
{{{60/20 - .5 = 60/(20+4)}}}
{{{3 - .5 = 60/24}}}
{{{5/2 = 5/2}}}
OK