1/8x-12=2x-1

Solution for 1/8x-12=2x-1 equation:

1/8x-12=2x-1

We move all terms to the left:

1/8x-12-(2x-1)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

1/8x-2x+1-12=0

We multiply all the terms by the denominator


-2x*8x+1*8x-12*8x+1=0

Wy multiply elements

-16x^2+8x-96x+1=0

We add all the numbers together, and all the variables

-16x^2-88x+1=0

a = -16; b = -88; c = +1;
Δ = b2-4ac
Δ = -882-4·(-16)·1
Δ = 7808
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:

$\sqrt{\Delta}=\sqrt{7808}=\sqrt{64*122}=\sqrt{64}*\sqrt{122}=8\sqrt{122}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-8\sqrt{122}}{2*-16}=\frac{88-8\sqrt{122}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+8\sqrt{122}}{2*-16}=\frac{88+8\sqrt{122}}{-32}
$