Question 215011
{{{42 = -21t + 4.9t^2}}} Start with the given equation.



{{{420 = -210t + 49t^2}}} Multiply EVERY term by 10 to make every value a whole number.



{{{0 = -210t + 49t^2-420}}} Subtract 420 from both sides.



{{{0 = 49t^2-210t-420}}} Rearrange the terms.



Notice that the quadratic {{{49t^2-210t-420}}} is in the form of {{{At^2+Bt+C}}} where {{{A=49}}}, {{{B=-210}}}, and {{{C=-420}}}



Let's use the quadratic formula to solve for "t":



{{{t = (-B +- sqrt( B^2-4AC ))/(2A)}}} Start with the quadratic formula



{{{t = (-(-210) +- sqrt( (-210)^2-4(49)(-420) ))/(2(49))}}} Plug in  {{{A=49}}}, {{{B=-210}}}, and {{{C=-420}}}



{{{t = (210 +- sqrt( (-210)^2-4(49)(-420) ))/(2(49))}}} Negate {{{-210}}} to get {{{210}}}. 



{{{t = (210 +- sqrt( 44100-4(49)(-420) ))/(2(49))}}} Square {{{-210}}} to get {{{44100}}}. 



{{{t = (210 +- sqrt( 44100--82320 ))/(2(49))}}} Multiply {{{4(49)(-420)}}} to get {{{-82320}}}



{{{t = (210 +- sqrt( 44100+82320 ))/(2(49))}}} Rewrite {{{sqrt(44100--82320)}}} as {{{sqrt(44100+82320)}}}



{{{t = (210 +- sqrt( 126420 ))/(2(49))}}} Add {{{44100}}} to {{{82320}}} to get {{{126420}}}



{{{t = (210 +- sqrt( 126420 ))/(98)}}} Multiply {{{2}}} and {{{49}}} to get {{{98}}}. 



{{{t = (210 +- 14*sqrt(645))/(98)}}} Simplify the square root  (note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  



{{{t = (210+14*sqrt(645))/(98)}}} or {{{t = (210-14*sqrt(645))/(98)}}} Break up the expression.  



So the solutions are {{{t = (210+14*sqrt(645))/(98)}}} or {{{t = (210-14*sqrt(645))/(98)}}} 



which approximate to {{{t=5.771}}} or {{{t=-1.485}}} 



I'm assuming that the variable 't' is time. If so, then just ignore the second solution (as a negative time doesn't make sense).