t=28/t+3

Solution for t=28/t+3 equation:

t=28/t+3

We move all terms to the left:

t-(28/t+3)=0


Domain of the equation: t+3)!=0

t∈R


We get rid of parentheses

t-28/t-3=0

We multiply all the terms by the denominator


t*t-3*t-28=0

We add all the numbers together, and all the variables

-3t+t*t-28=0

Wy multiply elements

t^2-3t-28=0

a = 1; b = -3; c = -28;
Δ = b2-4ac
Δ = -32-4·1·(-28)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-11}{2*1}=\frac{-8}{2}
=-4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+11}{2*1}=\frac{14}{2}
=7
$