Question 314267
Solve for the indicated letter. Solve the formula.
S = {{{1/3}}}{{{nr^2h + 4nrh}}} for r.
:
{{{1/3}}}{{{nr^2h + 4nrh}}} = S
Multiply by 3
{{{nr^2h + 3(4nrh)}}} = 3S
:
{{{nr^2h + 12nrh}}} = 3S
Factor out nh
nh(r^2 + 12r) = 3S
divide both sides by nh
r^2 + 12r = {{{(3S)/(nh)}}}
Arrange as a quadratic equation
r^2 + 12r - {{{(3S)/(nh)}}} = 0
Solve for r using the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
In this equation: x = r a=1; b=12; c=-{{{(3S)/(nh)}}}
{{{r = (-12 +- sqrt(12^2-4*1*((-3S)/(nh)) ))/(2*1) }}}
:
{{{r = (-12 +- sqrt(144-4((-3S)/(nh)) ))/2 }}}
:
{{{r = (-12 +- sqrt(144+4((3S)/(nh)) ))/2 }}}