Question 905889
you want to solve for t instead of v.


the original equation is:


v = 2u + 3t^2


subtract 3t^2 from both sides of the equation and subtract v from both sides of the equation to get:


-3t^2 = 2u - v


divide both sides of the equation by -3 to get:


t^2 = 2u/-3 - v/-3


simplify to get:


t^2 = -2u/3 + v/3


simplify further to get t^2 = (-2u+v)/3


take the square root of both sides of the equation to get:


t = plus or minus sqrt((-2u+v)/3)


problem is now solved for t instead of v.


you can confirm you did it correctly by seeing that both equations are compatible with each other.


here's what i did:


start with t = plus or minus sqrt((-2u+v)/3)


let v = 400 and let u = 50 and solve for t.
these numbers were chosen so that the solutions would be integers.


you get t = plus or minus 10


now start with v = 2u + 3t^2 (your original equation)


let u = 50 and t = plus or minus 10.


when t = 10, you get v = 100 + 3*100 = 400


when t = -10, you get v = 100 + 3*100 = 400


the two equations are compatible with each other which confirms that you did the translation from solving for v to solving for t successfully.