10-1/6x=x+17

Solution for 10-1/6x=x+17 equation:

10-1/6x=x+17

We move all terms to the left:

10-1/6x-(x+17)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

-1/6x-x-17+10=0

We multiply all the terms by the denominator


-x*6x-17*6x+10*6x-1=0

Wy multiply elements

-6x^2-102x+60x-1=0

We add all the numbers together, and all the variables

-6x^2-42x-1=0

a = -6; b = -42; c = -1;
Δ = b2-4ac
Δ = -422-4·(-6)·(-1)
Δ = 1740
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:

$\sqrt{\Delta}=\sqrt{1740}=\sqrt{4*435}=\sqrt{4}*\sqrt{435}=2\sqrt{435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{435}}{2*-6}=\frac{42-2\sqrt{435}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{435}}{2*-6}=\frac{42+2\sqrt{435}}{-12}
$