x/6x-10x=16

Solution for x/6x-10x=16 equation:

x/6x-10x=16

We move all terms to the left:

x/6x-10x-(16)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-10x+x/6x-16=0

We multiply all the terms by the denominator


-10x*6x+x-16*6x=0

We add all the numbers together, and all the variables

x-10x*6x-16*6x=0

Wy multiply elements

-60x^2+x-96x=0

We add all the numbers together, and all the variables

-60x^2-95x=0

a = -60; b = -95; c = 0;
Δ = b2-4ac
Δ = -952-4·(-60)·0
Δ = 9025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9025}=95$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-95)-95}{2*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95)+95}{2*-60}=\frac{190}{-120}
=-1+7/12
$