(2/3)(6t+12)=(28)

Solution for (2/3)(6t+12)=(28) equation:

(2/3)(6t+12)=(28)

We move all terms to the left:

(2/3)(6t+12)-((28))=0


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

t∈R


determiningTheFunctionDomain
(2/3)(6t+12)-28=0

We add all the numbers together, and all the variables

(+2/3)(6t+12)-28=0

We multiply parentheses ..

(+12t^2+2/3*12)-28=0

We multiply all the terms by the denominator


(+12t^2+2-28*3*12)=0

We get rid of parentheses

12t^2+2-28*3*12=0

We add all the numbers together, and all the variables

12t^2-1006=0

a = 12; b = 0; c = -1006;
Δ = b2-4ac
Δ = 02-4·12·(-1006)
Δ = 48288
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:

$\sqrt{\Delta}=\sqrt{48288}=\sqrt{16*3018}=\sqrt{16}*\sqrt{3018}=4\sqrt{3018}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3018}}{2*12}=\frac{0-4\sqrt{3018}}{24}
=-\frac{4\sqrt{3018}}{24}
=-\frac{\sqrt{3018}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3018}}{2*12}=\frac{0+4\sqrt{3018}}{24}
=\frac{4\sqrt{3018}}{24}
=\frac{\sqrt{3018}}{6}
$