1/4x=2x-6/3

Solution for 1/4x=2x-6/3 equation:

1/4x=2x-6/3

We move all terms to the left:

1/4x-(2x-6/3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/4x-2x+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -8; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-8)·1
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{6}}{2*-8}=\frac{-8-4\sqrt{6}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{6}}{2*-8}=\frac{-8+4\sqrt{6}}{-16}
$