1/8x+12=x-9

Solution for 1/8x+12=x-9 equation:

1/8x+12=x-9

We move all terms to the left:

1/8x+12-(x-9)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

1/8x-x+9+12=0

We multiply all the terms by the denominator


-x*8x+9*8x+12*8x+1=0

Wy multiply elements

-8x^2+72x+96x+1=0

We add all the numbers together, and all the variables

-8x^2+168x+1=0

a = -8; b = 168; c = +1;
Δ = b2-4ac
Δ = 1682-4·(-8)·1
Δ = 28256
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:

$\sqrt{\Delta}=\sqrt{28256}=\sqrt{16*1766}=\sqrt{16}*\sqrt{1766}=4\sqrt{1766}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-4\sqrt{1766}}{2*-8}=\frac{-168-4\sqrt{1766}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+4\sqrt{1766}}{2*-8}=\frac{-168+4\sqrt{1766}}{-16}
$