2x-1=1/2x+4

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

2x-1=1/2x+4

We move all terms to the left:

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


Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-8x-2x-1=0

We add all the numbers together, and all the variables

4x^2-10x-1=0

a = 4; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·4·(-1)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{29}}{2*4}=\frac{10-2\sqrt{29}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{29}}{2*4}=\frac{10+2\sqrt{29}}{8}
$