0.83t^2+7t-5=0

Solution for 0.83t^2+7t-5=0 equation:

Simplifying
0.83t2 + 7t + -5 = 0

Reorder the terms:
-5 + 7t + 0.83t2 = 0

Solving
-5 + 7t + 0.83t2 = 0

Solving for variable 't'.

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

Divide each side by '0.83'.
-6.024096386 + 8.43373494t + t2 = 0

Move the constant term to the right:

Add '6.024096386' to each side of the equation.
-6.024096386 + 8.43373494t + 6.024096386 + t2 = 0 + 6.024096386

Reorder the terms:
-6.024096386 + 6.024096386 + 8.43373494t + t2 = 0 + 6.024096386

Combine like terms: -6.024096386 + 6.024096386 = 0.000000000
0.000000000 + 8.43373494t + t2 = 0 + 6.024096386
8.43373494t + t2 = 0 + 6.024096386

Combine like terms: 0 + 6.024096386 = 6.024096386
8.43373494t + t2 = 6.024096386

The t term is 8.43373494t.  Take half its coefficient (4.21686747).
Square it (17.78197126) and add it to both sides.

Add '17.78197126' to each side of the equation.
8.43373494t + 17.78197126 + t2 = 6.024096386 + 17.78197126

Reorder the terms:
17.78197126 + 8.43373494t + t2 = 6.024096386 + 17.78197126

Combine like terms: 6.024096386 + 17.78197126 = 23.806067646
17.78197126 + 8.43373494t + t2 = 23.806067646

Factor a perfect square on the left side:
(t + 4.21686747)(t + 4.21686747) = 23.806067646

Calculate the square root of the right side: 4.879146201

Break this problem into two subproblems by setting 
(t + 4.21686747) equal to 4.879146201 and -4.879146201.

Subproblem 1
t + 4.21686747 = 4.879146201

Simplifying
t + 4.21686747 = 4.879146201

Reorder the terms:
4.21686747 + t = 4.879146201

Solving
4.21686747 + t = 4.879146201

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-4.21686747' to each side of the equation.
4.21686747 + -4.21686747 + t = 4.879146201 + -4.21686747

Combine like terms: 4.21686747 + -4.21686747 = 0.00000000
0.00000000 + t = 4.879146201 + -4.21686747
t = 4.879146201 + -4.21686747

Combine like terms: 4.879146201 + -4.21686747 = 0.662278731
t = 0.662278731

Simplifying
t = 0.662278731

Subproblem 2
t + 4.21686747 = -4.879146201

Simplifying
t + 4.21686747 = -4.879146201

Reorder the terms:
4.21686747 + t = -4.879146201

Solving
4.21686747 + t = -4.879146201

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-4.21686747' to each side of the equation.
4.21686747 + -4.21686747 + t = -4.879146201 + -4.21686747

Combine like terms: 4.21686747 + -4.21686747 = 0.00000000
0.00000000 + t = -4.879146201 + -4.21686747
t = -4.879146201 + -4.21686747

Combine like terms: -4.879146201 + -4.21686747 = -9.096013671
t = -9.096013671

Simplifying
t = -9.096013671

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.662278731, -9.096013671}