6t-9+1/t=15

Solution for 6t-9+1/t=15 equation:

6t-9+1/t=15

We move all terms to the left:

6t-9+1/t-(15)=0


Domain of the equation: t!=0

t∈R


We add all the numbers together, and all the variables

6t+1/t-24=0

We multiply all the terms by the denominator


6t*t-24*t+1=0

We add all the numbers together, and all the variables

-24t+6t*t+1=0

Wy multiply elements

6t^2-24t+1=0

a = 6; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·6·1
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{138}}{2*6}=\frac{24-2\sqrt{138}}{12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{138}}{2*6}=\frac{24+2\sqrt{138}}{12}
$