t=16/t-6

Solution for t=16/t-6 equation:

t=16/t-6

We move all terms to the left:

t-(16/t-6)=0


Domain of the equation: t-6)!=0

t∈R


We get rid of parentheses

t-16/t+6=0

We multiply all the terms by the denominator


t*t+6*t-16=0

We add all the numbers together, and all the variables

6t+t*t-16=0

Wy multiply elements

t^2+6t-16=0

a = 1; b = 6; c = -16;
Δ = b2-4ac
Δ = 62-4·1·(-16)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10}{2*1}=\frac{-16}{2}
=-8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10}{2*1}=\frac{4}{2}
=2
$