Question 845803
{{{(C*T)/2 = sqrt(L^2 + ((V*T)/2)^2)}}}


Raise both members to the 2 power ( meaning square both sides).
{{{(CT/2)^2=L^2 + ((V*T)/2)^2}}}


Add the additive inverse of {{{((VT)/2)^2}}} to both sides.
{{{(CT/2)^2-((VT)/2)^2=L^2}}}

Steps beyond here can vary but should be mostly consistent with this:


Apply rule of exponents for the left member.
{{{(C/2)^2*T^2-(V/2)^2*T^2=L^2}}}; notice the two terms of T^2 in the left member.


Combine like-terms, or think of it as the reverse of the Distributive Property.
{{{((C^2)/4-(V^2)/4)T^2=L^2}}}


Simplify the rational expression factor.
{{{((C^2-V^2)/4)T^2=L^2}}}


Multiply both members by multiplicative inverse of the rational expression
(Being shown more fully):
{{{(4/(C^2-V^2))((C^2-V^2)/4)T^2=(4/(C^2-V^2))L^2}}}
{{{1*T^2=(4L^2)/(C^2-V^2)}}}
{{{T^2=(4L^2)/(C^2-V^2)}}}


Raise both members to the {{{1/2}}} power.
{{{highlight(highlight(highlight(T=2L/sqrt(C^2-V^2))))}}}
.
and to be strictly correct...  OR {{{highlight(T=-2L/sqrt(C^2-V^2))}}}.
Both of them are solved for T.



A few minor steps may have been omitted, because they might seem as too obvious and unnecessary to be shown, but these as shown should be clear enough for your understanding.
-
Note also, some people may not want an irrational expression in the denominator and so would want to rationalize the denominator.