5t+t(1.2-t)=90

Solution for 5t+t(1.2-t)=90 equation:

Simplifying
5t + t(1.2 + -1t) = 90
5t + (1.2 * t + -1t * t) = 90
5t + (1.2t + -1t2) = 90

Combine like terms: 5t + 1.2t = 6.2t
6.2t + -1t2 = 90

Solving
6.2t + -1t2 = 90

Solving for variable 't'.

Reorder the terms:
-90 + 6.2t + -1t2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 6.2t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
90 + -6.2t + t2 = 0

Move the constant term to the right:

Add '-90' to each side of the equation.
90 + -6.2t + -90 + t2 = 0 + -90

Reorder the terms:
90 + -90 + -6.2t + t2 = 0 + -90

Combine like terms: 90 + -90 = 0
0 + -6.2t + t2 = 0 + -90
-6.2t + t2 = 0 + -90

Combine like terms: 0 + -90 = -90
-6.2t + t2 = -90

The t term is -6.2t.  Take half its coefficient (-3.1).
Square it (9.61) and add it to both sides.

Add '9.61' to each side of the equation.
-6.2t + 9.61 + t2 = -90 + 9.61

Reorder the terms:
9.61 + -6.2t + t2 = -90 + 9.61

Combine like terms: -90 + 9.61 = -80.39
9.61 + -6.2t + t2 = -80.39

Factor a perfect square on the left side:
(t + -3.1)(t + -3.1) = -80.39

Can't calculate square root of the right side.

The solution to this equation could not be determined.