125/6x=14x+1/6x=

Solution for 125/6x=14x+1/6x= equation:

125/6x=14x+1/6x=

We move all terms to the left:

125/6x-(14x+1/6x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

125/6x-(+14x+1/6x)=0

We get rid of parentheses

125/6x-14x-1/6x=0

We multiply all the terms by the denominator


-14x*6x+125-1=0

We add all the numbers together, and all the variables

-14x*6x+124=0

Wy multiply elements

-84x^2+124=0

a = -84; b = 0; c = +124;
Δ = b2-4ac
Δ = 02-4·(-84)·124
Δ = 41664
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:

$\sqrt{\Delta}=\sqrt{41664}=\sqrt{64*651}=\sqrt{64}*\sqrt{651}=8\sqrt{651}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{651}}{2*-84}=\frac{0-8\sqrt{651}}{-168}
=-\frac{8\sqrt{651}}{-168}
=-\frac{\sqrt{651}}{-21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{651}}{2*-84}=\frac{0+8\sqrt{651}}{-168}
=\frac{8\sqrt{651}}{-168}
=\frac{\sqrt{651}}{-21}
$