5-6x/8x+17=x

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

5-6x/8x+17=x

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-1x-6x/8x+22=0

We multiply all the terms by the denominator


-1x*8x-6x+22*8x=0

We add all the numbers together, and all the variables

-6x-1x*8x+22*8x=0

Wy multiply elements

-8x^2-6x+176x=0

We add all the numbers together, and all the variables

-8x^2+170x=0

a = -8; b = 170; c = 0;
Δ = b2-4ac
Δ = 1702-4·(-8)·0
Δ = 28900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28900}=170$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(170)-170}{2*-8}=\frac{-340}{-16}
=21+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(170)+170}{2*-8}=\frac{0}{-16}
=0
$