1/8x+7=x

Solution for 1/8x+7=x equation:

1/8x+7=x

We move all terms to the left:

1/8x+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+1/8x+7=0

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2+56x+1=0

a = -8; b = 56; c = +1;
Δ = b2-4ac
Δ = 562-4·(-8)·1
Δ = 3168
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:

$\sqrt{\Delta}=\sqrt{3168}=\sqrt{144*22}=\sqrt{144}*\sqrt{22}=12\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-12\sqrt{22}}{2*-8}=\frac{-56-12\sqrt{22}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+12\sqrt{22}}{2*-8}=\frac{-56+12\sqrt{22}}{-16}
$