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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-14x*6x+1x*6x+126=0

Wy multiply elements

-84x^2+6x^2+126=0

We add all the numbers together, and all the variables

-78x^2+126=0

a = -78; b = 0; c = +126;
Δ = b2-4ac
Δ = 02-4·(-78)·126
Δ = 39312
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:

$\sqrt{\Delta}=\sqrt{39312}=\sqrt{144*273}=\sqrt{144}*\sqrt{273}=12\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{273}}{2*-78}=\frac{0-12\sqrt{273}}{-156}
=-\frac{12\sqrt{273}}{-156}
=-\frac{\sqrt{273}}{-13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{273}}{2*-78}=\frac{0+12\sqrt{273}}{-156}
=\frac{12\sqrt{273}}{-156}
=\frac{\sqrt{273}}{-13}
$