x^2-8x/6=x

Solution for x^2-8x/6=x equation:

x^2-8x/6=x

We move all terms to the left:

x^2-8x/6-(x)=0

We add all the numbers together, and all the variables

x^2-1x-8x/6=0

We multiply all the terms by the denominator


x^2*6-1x*6-8x=0

We add all the numbers together, and all the variables

x^2*6-8x-1x*6=0

Wy multiply elements

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

We add all the numbers together, and all the variables

6x^2-14x=0

a = 6; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·6·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*6}=\frac{28}{12}
=2+1/3
$