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

Solution for 125/6x-14x+1/6x=0 equation:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-14x+125/6x+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+126=0

Wy multiply elements

-84x^2+126=0

a = -84; b = 0; c = +126;
Δ = b2-4ac
Δ = 02-4·(-84)·126
Δ = 42336
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:

$\sqrt{\Delta}=\sqrt{42336}=\sqrt{7056*6}=\sqrt{7056}*\sqrt{6}=84\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-84\sqrt{6}}{2*-84}=\frac{0-84\sqrt{6}}{-168}
=-\frac{84\sqrt{6}}{-168}
=-\frac{\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+84\sqrt{6}}{2*-84}=\frac{0+84\sqrt{6}}{-168}
=\frac{84\sqrt{6}}{-168}
=\frac{\sqrt{6}}{-2}
$