10x-54=34/6x

Solution for 10x-54=34/6x equation:

10x-54=34/6x

We move all terms to the left:

10x-54-(34/6x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10x-(+34/6x)-54=0

We get rid of parentheses

10x-34/6x-54=0

We multiply all the terms by the denominator


10x*6x-54*6x-34=0

Wy multiply elements

60x^2-324x-34=0

a = 60; b = -324; c = -34;
Δ = b2-4ac
Δ = -3242-4·60·(-34)
Δ = 113136
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:

$\sqrt{\Delta}=\sqrt{113136}=\sqrt{16*7071}=\sqrt{16}*\sqrt{7071}=4\sqrt{7071}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-324)-4\sqrt{7071}}{2*60}=\frac{324-4\sqrt{7071}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-324)+4\sqrt{7071}}{2*60}=\frac{324+4\sqrt{7071}}{120}
$