(7/3)t=84

Solution for (7/3)t=84 equation:

(7/3)t=84

We move all terms to the left:

(7/3)t-(84)=0


Domain of the equation: 3)t!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

(+7/3)t-84=0

We multiply parentheses

7t^2-84=0

a = 7; b = 0; c = -84;
Δ = b2-4ac
Δ = 02-4·7·(-84)
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{3}}{2*7}=\frac{0-28\sqrt{3}}{14}
=-\frac{28\sqrt{3}}{14}
=-2\sqrt{3}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{3}}{2*7}=\frac{0+28\sqrt{3}}{14}
=\frac{28\sqrt{3}}{14}
=2\sqrt{3}
$