1/2x+12=8x

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

1/2x+12=8x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -16; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·(-16)·1
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{10}}{2*-16}=\frac{-24-8\sqrt{10}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{10}}{2*-16}=\frac{-24+8\sqrt{10}}{-32}
$