17(3x-1)=21/2x

Solution for 17(3x-1)=21/2x equation:

17(3x-1)=21/2x

We move all terms to the left:

17(3x-1)-(21/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

17(3x-1)-(+21/2x)=0

We multiply parentheses

51x-(+21/2x)-17=0

We get rid of parentheses

51x-21/2x-17=0

We multiply all the terms by the denominator


51x*2x-17*2x-21=0

Wy multiply elements

102x^2-34x-21=0

a = 102; b = -34; c = -21;
Δ = b2-4ac
Δ = -342-4·102·(-21)
Δ = 9724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9724}=\sqrt{4*2431}=\sqrt{4}*\sqrt{2431}=2\sqrt{2431}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{2431}}{2*102}=\frac{34-2\sqrt{2431}}{204}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{2431}}{2*102}=\frac{34+2\sqrt{2431}}{204}
$