t+4/3t=84

Solution for t+4/3t=84 equation:

t+4/3t=84

We move all terms to the left:

t+4/3t-(84)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We multiply all the terms by the denominator


t*3t-84*3t+4=0

Wy multiply elements

3t^2-252t+4=0

a = 3; b = -252; c = +4;
Δ = b2-4ac
Δ = -2522-4·3·4
Δ = 63456
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:

$\sqrt{\Delta}=\sqrt{63456}=\sqrt{16*3966}=\sqrt{16}*\sqrt{3966}=4\sqrt{3966}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-252)-4\sqrt{3966}}{2*3}=\frac{252-4\sqrt{3966}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-252)+4\sqrt{3966}}{2*3}=\frac{252+4\sqrt{3966}}{6}
$