3t^2-12t+7=0

Simple and best practice solution for 3t^2-12t+7=0 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 3t^2-12t+7=0 equation: 


Simplifying
3t2 + -12t + 7 = 0

Reorder the terms:
7 + -12t + 3t2 = 0

Solving
7 + -12t + 3t2 = 0

Solving for variable 't'.

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

Divide each side by '3'.
2.333333333 + -4t + t2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -4t + -2.333333333 + t2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -4t + t2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -4t + t2 = 0 + -2.333333333
-4t + t2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-4t + t2 = -2.333333333

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = -2.333333333 + 4

Reorder the terms:
4 + -4t + t2 = -2.333333333 + 4

Combine like terms: -2.333333333 + 4 = 1.666666667
4 + -4t + t2 = 1.666666667

Factor a perfect square on the left side:
(t + -2)(t + -2) = 1.666666667

Calculate the square root of the right side: 1.290994449

Break this problem into two subproblems by setting 
(t + -2) equal to 1.290994449 and -1.290994449.


Subproblem 1
t + -2 = 1.290994449

Simplifying
t + -2 = 1.290994449

Reorder the terms:
-2 + t = 1.290994449

Solving
-2 + t = 1.290994449

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = 1.290994449 + 2

Combine like terms: -2 + 2 = 0
0 + t = 1.290994449 + 2
t = 1.290994449 + 2

Combine like terms: 1.290994449 + 2 = 3.290994449
t = 3.290994449

Simplifying
t = 3.290994449


Subproblem 2
t + -2 = -1.290994449

Simplifying
t + -2 = -1.290994449

Reorder the terms:
-2 + t = -1.290994449

Solving
-2 + t = -1.290994449

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = -1.290994449 + 2

Combine like terms: -2 + 2 = 0
0 + t = -1.290994449 + 2
t = -1.290994449 + 2

Combine like terms: -1.290994449 + 2 = 0.709005551
t = 0.709005551

Simplifying
t = 0.709005551


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.290994449, 0.709005551}

See similar equations:

| 8y-11=-12y+8 | | a-1= | | 1.2=24 | | -2(3x-(1))=3x+(-3) | | 31=X+13 | | 2x+2+34=-4x | | -1+3x=-27 | | 95=-4x+3(5x-5) | | Y-4=6y+26 | | -3x+12=-3x+12 | | 7-j+5j=9 | | -3x-3=-33 | | 7+7p+16-3p= | | 6x+30=6x+11 | | 7-4y=4y-7 | | 12w+6=10 | | 79=6x+2x+7 | | -4w-4=-25 | | -7(-6w-2u+5)= | | -3+2s=8 | | 14x+2.40=8.70 | | 9(x+3)=x-3 | | 34=-2(1-7x)-5x | | -6+7x=92 | | a-0.004=240 | | Y+2=5+4y | | 6+9x=3x | | -3b+4x=-6 | | 2t+7=7 | | -21=7-4 | | 5x-4+x=-10 | | 2y+1=y+11 |

Equations solver categories