(1/3)(6t+12)=-3(2+-4)

Solution for (1/3)(6t+12)=-3(2+-4) equation:

(1/3)(6t+12)=-3(2+-4)

We move all terms to the left:

(1/3)(6t+12)-(-3(2+-4))=0


Domain of the equation: 3)(6t+12)!=0

t∈R


We add all the numbers together, and all the variables

(+1/3)(6t+12)-(-3(-2))=0

We add all the numbers together, and all the variables

(+1/3)(6t+12)-6=0

We multiply parentheses ..

(+6t^2+1/3*12)-6=0

We multiply all the terms by the denominator


(+6t^2+1-6*3*12)=0

We get rid of parentheses

6t^2+1-6*3*12=0

We add all the numbers together, and all the variables

6t^2-215=0

a = 6; b = 0; c = -215;
Δ = b2-4ac
Δ = 02-4·6·(-215)
Δ = 5160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5160}=\sqrt{4*1290}=\sqrt{4}*\sqrt{1290}=2\sqrt{1290}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1290}}{2*6}=\frac{0-2\sqrt{1290}}{12}
=-\frac{2\sqrt{1290}}{12}
=-\frac{\sqrt{1290}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1290}}{2*6}=\frac{0+2\sqrt{1290}}{12}
=\frac{2\sqrt{1290}}{12}
=\frac{\sqrt{1290}}{6}
$