6t^2+13t=6

Simple and best practice solution for 6t^2+13t=6 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 6t^2+13t=6 equation:


Simplifying
6t2 + 13t = 6

Reorder the terms:
13t + 6t2 = 6

Solving
13t + 6t2 = 6

Solving for variable 't'.

Reorder the terms:
-6 + 13t + 6t2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 13t + 6t2 = 0

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

Divide each side by '6'.
-1 + 2.166666667t + t2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2.166666667t + 1 + t2 = 0 + 1

Reorder the terms:
-1 + 1 + 2.166666667t + t2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2.166666667t + t2 = 0 + 1
2.166666667t + t2 = 0 + 1

Combine like terms: 0 + 1 = 1
2.166666667t + t2 = 1

The t term is 2.166666667t.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667t + 1.173611113 + t2 = 1 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667t + t2 = 1 + 1.173611113

Combine like terms: 1 + 1.173611113 = 2.173611113
1.173611113 + 2.166666667t + t2 = 2.173611113

Factor a perfect square on the left side:
(t + 1.083333334)(t + 1.083333334) = 2.173611113

Calculate the square root of the right side: 1.474317168

Break this problem into two subproblems by setting 
(t + 1.083333334) equal to 1.474317168 and -1.474317168.

Subproblem 1

t + 1.083333334 = 1.474317168 Simplifying t + 1.083333334 = 1.474317168 Reorder the terms: 1.083333334 + t = 1.474317168 Solving 1.083333334 + t = 1.474317168 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + t = 1.474317168 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + t = 1.474317168 + -1.083333334 t = 1.474317168 + -1.083333334 Combine like terms: 1.474317168 + -1.083333334 = 0.390983834 t = 0.390983834 Simplifying t = 0.390983834

Subproblem 2

t + 1.083333334 = -1.474317168 Simplifying t + 1.083333334 = -1.474317168 Reorder the terms: 1.083333334 + t = -1.474317168 Solving 1.083333334 + t = -1.474317168 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + t = -1.474317168 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + t = -1.474317168 + -1.083333334 t = -1.474317168 + -1.083333334 Combine like terms: -1.474317168 + -1.083333334 = -2.557650502 t = -2.557650502 Simplifying t = -2.557650502

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.390983834, -2.557650502}

See similar equations:

| 2(3x+6)=3(3x+2) | | X^2-28x+100=0 | | x/4+6=-12 | | 9/11/9/11 | | 3m^2+19m+6=0 | | 6x+4=-1 | | 2.35x+1.1=x-8.62 | | 3y+6=-99 | | k^2-10k-24=0 | | 20x-8=4(4x-9) | | 4+4y=-20 | | 2x+7=1-4x | | 21/8*4/9 | | 2-3x=4x+17 | | 5=10-x | | 2.6x=-12.532 | | h-1/6h+3(2h^2+9h+4) | | 5.3x+2=12.7x-2 | | 7/8z=1/4 | | h-1/6h+3*(2h^2+9h+4) | | 3(x-2)+3(2x+2)=-3(2-x) | | 4p+3=2p+5 | | 5/9y=-35/81 | | 8(y-2)=4y-32 | | A/5+8=5 | | 8x^2-17x+2=0 | | 3x^2+6x+77=0 | | 9x-z(7x-1)=2 | | 3.2x+6.57=-21.91 | | -2*-2.5-4=1.5*-2.5+7 | | Y/9-2=5 | | 5x-7y=16fory |

Equations solver categories