5-17/6x+8x=x

Solution for 5-17/6x+8x=x equation:

5-17/6x+8x=x

We move all terms to the left:

5-17/6x+8x-(x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

7x-17/6x+5=0

We multiply all the terms by the denominator


7x*6x+5*6x-17=0

Wy multiply elements

42x^2+30x-17=0

a = 42; b = 30; c = -17;
Δ = b2-4ac
Δ = 302-4·42·(-17)
Δ = 3756
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:

$\sqrt{\Delta}=\sqrt{3756}=\sqrt{4*939}=\sqrt{4}*\sqrt{939}=2\sqrt{939}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{939}}{2*42}=\frac{-30-2\sqrt{939}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{939}}{2*42}=\frac{-30+2\sqrt{939}}{84}
$