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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -8; b = 2; c = +2;
Δ = b2-4ac
Δ = 22-4·(-8)·2
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{17}}{2*-8}=\frac{-2-2\sqrt{17}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{17}}{2*-8}=\frac{-2+2\sqrt{17}}{-16}
$