Question 342563
solve the equation B = 3K / (2B-1) for the variable B.
:
B = {{{(3K)/((2B-1))}}}
Multiply both sides by (2B-1)
B(2B-1) = 3k
2B^2 - B = 3k
:
A quadratic equation
2B^2 - B - 3k = 0
Use the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
But in this problem x=B; a=2; b=-1 c=-3k
{{{B = (-(-1) +- sqrt(-1^2-4*2*(-3k) ))/(2*2) }}}
:
{{{B = (1 +- sqrt(1 - (-24k) ))/4 }}}
Two solutions
{{{B = (1 + sqrt(1 + 24k ))/4 }}}
and
{{{B = (1 - sqrt(1 + 24k ))/4 }}}