1/8x+140=x

Solution for 1/8x+140=x equation:

1/8x+140=x

We move all terms to the left:

1/8x+140-(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+140=0

We multiply all the terms by the denominator


-1x*8x+140*8x+1=0

Wy multiply elements

-8x^2+1120x+1=0

a = -8; b = 1120; c = +1;
Δ = b2-4ac
Δ = 11202-4·(-8)·1
Δ = 1254432
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:

$\sqrt{\Delta}=\sqrt{1254432}=\sqrt{16*78402}=\sqrt{16}*\sqrt{78402}=4\sqrt{78402}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1120)-4\sqrt{78402}}{2*-8}=\frac{-1120-4\sqrt{78402}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1120)+4\sqrt{78402}}{2*-8}=\frac{-1120+4\sqrt{78402}}{-16}
$