text: # Solve for t (4t^2)/5=(3t)/5+27/10
  
  4t25=3t5+2710
  Multiply both sides of the equation by 5.
  4t2=3t5⋅(5)+2710⋅(5)
  Simplify each term.
  Cancel the common factor of 5.
  Cancel the common factor.
  4t2=3t5⋅5+2710⋅(5)
  Rewrite the expression.
  4t2=3t+2710⋅(5)
  4t2=3t+2710⋅(5)
  Cancel the common factor of 5.
  Factor 5 out of 10.
  4t2=3t+275(2)⋅5
  Cancel the common factor.
  4t2=3t+275⋅2⋅5
  Rewrite the expression.
  4t2=3t+272
  4t2=3t+272
  4t2=3t+272
  Subtract 3t from both sides of the equation.
  4t2-3t=272
  Move 272 to the left side of the equation by subtracting it from both sides.
  4t2-3t-272=0
  Multiply through by the least common denominator 2, then simplify.
  Apply the distributive property.
  2(4t2)+2(-3t)+2(-272)=0
  Simplify.
  Multiply 4 by 2.
  8t2+2(-3t)+2(-272)=0
  Multiply -3 by 2.
  8t2-6t+2(-272)=0
  Cancel the common factor of 2.
  Move the leading negative in -272 into the numerator.
  8t2-6t+2(-272)=0
  Cancel the common factor.
  8t2-6t+2(-272)=0
  Rewrite the expression.
  8t2-6t-27=0
  8t2-6t-27=0
  8t2-6t-27=0
  8t2-6t-27=0
  Use the quadratic formula to find the solutions.
  -b±b2-4(ac)2a
  Substitute the values a=8, b=-6, and c=-27 into the quadratic formula and solve for t.
  6±(-6)2-4⋅(8⋅-27)2⋅8
  Simplify.
  Simplify the numerator.
  Raise -6 to the power of 2.
  t=6±36-4⋅(8⋅-27)2⋅8
  Multiply 8 by -27.
  t=6±36-4⋅-2162⋅8
  Multiply -4 by -216.
  t=6±36+8642⋅8
  t=6±9002⋅8
  Rewrite 900 as 302.
  t=6±3022⋅8
  Pull terms out from under the radical, assuming positive real numbers.
  t=6±302⋅8
  t=6±302⋅8
  Multiply 2 by 8.
  t=6±3016
  Simplify 6±3016.
  t=3±158
  t=3±158
  The final answer is the combination of both solutions.
  t=94,-32
  The result can be shown in multiple forms.
  Exact Form:
  t=94,-32
  Decimal Form:
  t=2.25,-1.5
  Mixed Number Form:
  t=214,-112
  Solve for t (4t^2)/5=(3t)/5+27/10