t+2/3t=40

Solution for t+2/3t=40 equation:

t+2/3t=40

We move all terms to the left:

t+2/3t-(40)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We multiply all the terms by the denominator


t*3t-40*3t+2=0

Wy multiply elements

3t^2-120t+2=0

a = 3; b = -120; c = +2;
Δ = b2-4ac
Δ = -1202-4·3·2
Δ = 14376
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:

$\sqrt{\Delta}=\sqrt{14376}=\sqrt{4*3594}=\sqrt{4}*\sqrt{3594}=2\sqrt{3594}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-2\sqrt{3594}}{2*3}=\frac{120-2\sqrt{3594}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+2\sqrt{3594}}{2*3}=\frac{120+2\sqrt{3594}}{6}
$