57t+1/3t-27=17

Solution for 57t+1/3t-27=17 equation:

57t+1/3t-27=17

We move all terms to the left:

57t+1/3t-27-(17)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We add all the numbers together, and all the variables

57t+1/3t-44=0

We multiply all the terms by the denominator


57t*3t-44*3t+1=0

Wy multiply elements

171t^2-132t+1=0

a = 171; b = -132; c = +1;
Δ = b2-4ac
Δ = -1322-4·171·1
Δ = 16740
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:

$\sqrt{\Delta}=\sqrt{16740}=\sqrt{36*465}=\sqrt{36}*\sqrt{465}=6\sqrt{465}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-6\sqrt{465}}{2*171}=\frac{132-6\sqrt{465}}{342}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+6\sqrt{465}}{2*171}=\frac{132+6\sqrt{465}}{342}
$