1/2x+8=12x

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

1/2x+8=12x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-24x^2+16x+1=0

a = -24; b = 16; c = +1;
Δ = b2-4ac
Δ = 162-4·(-24)·1
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{22}}{2*-24}=\frac{-16-4\sqrt{22}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{22}}{2*-24}=\frac{-16+4\sqrt{22}}{-48}
$