/3x-10x+6=1x

Solution for /3x-10x+6=1x equation:

/3x-10x+6=1x

We move all terms to the left:

/3x-10x+6-(1x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-11x+/3x+6=0

We multiply all the terms by the denominator


-11x*3x+6*3x+=0

We add all the numbers together, and all the variables

-11x*3x+6*3x=0

Wy multiply elements

-33x^2+18x=0

a = -33; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-33)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-33}=\frac{-36}{-66}
=6/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-33}=\frac{0}{-66}
=0
$