1/2x+4=6x

Solution for 1/2x+4=6x equation:

1/2x+4=6x

We move all terms to the left:

1/2x+4-(6x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-6x+1/2x+4=0

We multiply all the terms by the denominator


-6x*2x+4*2x+1=0

Wy multiply elements

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

a = -12; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-12)·1
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{7}}{2*-12}=\frac{-8-4\sqrt{7}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{7}}{2*-12}=\frac{-8+4\sqrt{7}}{-24}
$