-17+1/3x=6x

Solution for -17+1/3x=6x equation:

-17+1/3x=6x

We move all terms to the left:

-17+1/3x-(6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-6x+1/3x-17=0

We multiply all the terms by the denominator


-6x*3x-17*3x+1=0

Wy multiply elements

-18x^2-51x+1=0

a = -18; b = -51; c = +1;
Δ = b2-4ac
Δ = -512-4·(-18)·1
Δ = 2673
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:

$\sqrt{\Delta}=\sqrt{2673}=\sqrt{81*33}=\sqrt{81}*\sqrt{33}=9\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-9\sqrt{33}}{2*-18}=\frac{51-9\sqrt{33}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+9\sqrt{33}}{2*-18}=\frac{51+9\sqrt{33}}{-36}
$