16t^2 - 12t - h = 016t2−12t−h=0
you would need to complete the square:
ax^2+bx +cax2+bx+c
a=1a=1
c=(1/2b)^2c=(12b)2
So first move the hh over:
16t^2 - 12t = h16t2−12t=h
now divide by 16 so a=1a=1
(16t^2 - 12t)/16 = h/1616t2−12t16=h16
t^2 - 3/4t = h/16t2−34t=h16
now we are ready to complete the square:
t^2 - 3/4t +c = h/16 +ct2−34t+c=h16+c
c=(1/2b)^2c=(12b)2
c=(1/2*-3/4)^2 = 9/64c=(12⋅−34)2=964
t^2 - 3/4t +9/64 = h/16 +9/64t2−34t+964=h16+964
(t-3/8)^2 = h/16 +9/64(t−38)2=h16+964
sqrt((t-3/8)^2)=+-sqrt( h/16 +9/64)√(t−38)2=±√h16+964
t-3/8=+-sqrt( h/16 +9/64)t−38=±√h16+964
t=3/8+-sqrt( h/16 +9/64)t=38±√h16+964
t=3/8+-sqrt( (4h)/64 +9/64)t=38±√4h64+964
t=3/8+-sqrt( (4h+9)/64)t=38±√4h+964
t=3/8+-sqrt( (4h+9))/8t=38±√(4h+9)8
t=(3+-sqrt( 4h+9))/8t=3±√4h+98
