1/2x=4x+8

Solution for 1/2x=4x+8 equation:

1/2x=4x+8

We move all terms to the left:

1/2x-(4x+8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-4x-8=0

We multiply all the terms by the denominator


-4x*2x-8*2x+1=0

Wy multiply elements

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

a = -8; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·(-8)·1
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-12\sqrt{2}}{2*-8}=\frac{16-12\sqrt{2}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+12\sqrt{2}}{2*-8}=\frac{16+12\sqrt{2}}{-16}
$