2t+15/t=92

Solution for 2t+15/t=92 equation:

2t+15/t=92

We move all terms to the left:

2t+15/t-(92)=0


Domain of the equation: t!=0

t∈R


We multiply all the terms by the denominator


2t*t-92*t+15=0

We add all the numbers together, and all the variables

-92t+2t*t+15=0

Wy multiply elements

2t^2-92t+15=0

a = 2; b = -92; c = +15;
Δ = b2-4ac
Δ = -922-4·2·15
Δ = 8344
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:

$\sqrt{\Delta}=\sqrt{8344}=\sqrt{4*2086}=\sqrt{4}*\sqrt{2086}=2\sqrt{2086}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-2\sqrt{2086}}{2*2}=\frac{92-2\sqrt{2086}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+2\sqrt{2086}}{2*2}=\frac{92+2\sqrt{2086}}{4}
$