-9+x=1/8x-23

Solution for -9+x=1/8x-23 equation:

-9+x=1/8x-23

We move all terms to the left:

-9+x-(1/8x-23)=0


Domain of the equation: 8x-23)!=0

x∈R


We get rid of parentheses

x-1/8x+23-9=0

We multiply all the terms by the denominator


x*8x+23*8x-9*8x-1=0

Wy multiply elements

8x^2+184x-72x-1=0

We add all the numbers together, and all the variables

8x^2+112x-1=0

a = 8; b = 112; c = -1;
Δ = b2-4ac
Δ = 1122-4·8·(-1)
Δ = 12576
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:

$\sqrt{\Delta}=\sqrt{12576}=\sqrt{16*786}=\sqrt{16}*\sqrt{786}=4\sqrt{786}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-4\sqrt{786}}{2*8}=\frac{-112-4\sqrt{786}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+4\sqrt{786}}{2*8}=\frac{-112+4\sqrt{786}}{16}
$