8x-12=(1/2x-6)

Solution for 8x-12=(1/2x-6) equation:

8x-12=(1/2x-6)

We move all terms to the left:

8x-12-((1/2x-6))=0


Domain of the equation: 2x-6))!=0

x∈R


We multiply all the terms by the denominator


8x*2x-12*2x-6))-((1-6))=0

We add all the numbers together, and all the variables

8x*2x-12*2x-6))-((-5))=0

We add all the numbers together, and all the variables

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

Wy multiply elements

16x^2-24x=0

a = 16; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·16·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*16}=\frac{48}{32}
=1+1/2
$