1/8x+15=x

Solution for 1/8x+15=x equation:

1/8x+15=x

We move all terms to the left:

1/8x+15-(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+15=0

We multiply all the terms by the denominator


-1x*8x+15*8x+1=0

Wy multiply elements

-8x^2+120x+1=0

a = -8; b = 120; c = +1;
Δ = b2-4ac
Δ = 1202-4·(-8)·1
Δ = 14432
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:

$\sqrt{\Delta}=\sqrt{14432}=\sqrt{16*902}=\sqrt{16}*\sqrt{902}=4\sqrt{902}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-4\sqrt{902}}{2*-8}=\frac{-120-4\sqrt{902}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+4\sqrt{902}}{2*-8}=\frac{-120+4\sqrt{902}}{-16}
$