Question 442077
{{{(1/2)x^2-(1/2)x-15/32=0}}}........LCD is {{{32}}}

{{{(1/2)x^2*32-(1/2)x*32-15*32/32=0}}}

{{{(1/cross(2))cross(32)*16x^2-(1/cross(2))*cross(32)16x-15*cross(32)/cross(32)=0}}}


{{{16x^2-16x-15=0}}}....use quadratic formula to fine other two solutions

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}..notice that {{{a=16}}}, {{{b=-16}}} and {{{c=-15}}}


{{{x = (-(-16) +- sqrt( (-16)^2-4*16*(-15) ))/(2*16) }}}


{{{x = (16 +- sqrt( 256+960 ))/32 }}}


{{{x = (16 +- sqrt( 1216 ))/32 }}}


{{{x = (16 +- 34.87)/32 }}}

{{{x1 = (16 + 34.87)/32 }}}

{{{x1 = 50.87/32 }}}


{{{x1 = 1.5896875 }}}



{{{x2 = (16 - 34.87)/32 }}}

{{{x2 = -18.87/32 }}}


{{{x2 = -0.5896875 }}}


check:

{{{x1 = 1.5896875 }}}

{{{(1/2)(1.5896875)^2-(1/2)(1.5896875)-15/32=0}}}

{{{(1/2)(2.52710)-(1/2)(1.5896)-0.4687=0}}}

{{{(1.26355)-(0.7948)-0.4687=0}}}

{{{(0.46875)-0.4687=0}}}

{{{0=0}}}