2t=6/t-4

Solution for 2t=6/t-4 equation:

2t=6/t-4

We move all terms to the left:

2t-(6/t-4)=0


Domain of the equation: t-4)!=0

t∈R


We get rid of parentheses

2t-6/t+4=0

We multiply all the terms by the denominator


2t*t+4*t-6=0

We add all the numbers together, and all the variables

4t+2t*t-6=0

Wy multiply elements

2t^2+4t-6=0

a = 2; b = 4; c = -6;
Δ = b2-4ac
Δ = 42-4·2·(-6)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*2}=\frac{-12}{4}
=-3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*2}=\frac{4}{4}
=1
$