Question 70657
solve for Z: 3/2z^2=4z+1
:
Arrange as a quadratic equation:
1.5z^2 - 4z - 1 = 0
:
Using the quadratic formula; a = 1.5, b = -4, c = -1:
{{{z = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
:
{{{z = (-(-4) +- sqrt( -4^2 - 4 * 1.5 * -1 ))/(2*1.5) }}}
:
{{{z = (+4 +- sqrt( 16 - (-6) ))/(3) }}}
:
{{{z = (4 +- sqrt( 16 + 6))/(3) }}}
:
{{{z = (4 +- sqrt(22))/(3) }}}
:
{{{z = (4 +- 4.69)/(3) }}}
:
Solution 1:
{{{z = 8.69/3}}}
z = +2.9
:
Solution 2:
{{{z = -.69/3}}}
z = -.23