2/8x-7=x

Solution for 2/8x-7=x equation:

2/8x-7=x

We move all terms to the left:

2/8x-7-(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+2/8x-7=0

We multiply all the terms by the denominator


-1x*8x-7*8x+2=0

Wy multiply elements

-8x^2-56x+2=0

a = -8; b = -56; c = +2;
Δ = b2-4ac
Δ = -562-4·(-8)·2
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-40\sqrt{2}}{2*-8}=\frac{56-40\sqrt{2}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+40\sqrt{2}}{2*-8}=\frac{56+40\sqrt{2}}{-16}
$