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

Solution for (1/4)*x-1=2x equation:

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

We move all terms to the left:

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


Domain of the equation: 4)*x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

x^2-2x-1=0

a = 1; b = -2; c = -1;
Δ = b2-4ac
Δ = -22-4·1·(-1)
Δ = 8
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:

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