1/4x+6=2x

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

1/4x+6=2x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2+24x+1=0

a = -8; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·(-8)·1
Δ = 608
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:

$\sqrt{\Delta}=\sqrt{608}=\sqrt{16*38}=\sqrt{16}*\sqrt{38}=4\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{38}}{2*-8}=\frac{-24-4\sqrt{38}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{38}}{2*-8}=\frac{-24+4\sqrt{38}}{-16}
$