2x-1=1/2x+3,5=

Solution for 2x-1=1/2x+3,5= equation:

2x-1=1/2x+3.5=

We move all terms to the left:

2x-1-(1/2x+3.5)=0


Domain of the equation: 2x+3.5)!=0

x∈R


We get rid of parentheses

2x-1/2x-3.5-1=0

We multiply all the terms by the denominator


2x*2x-(3.5)*2x-1*2x-1=0

We multiply parentheses

2x*2x-7x-1*2x-1=0

Wy multiply elements

4x^2-7x-2x-1=0

We add all the numbers together, and all the variables

4x^2-9x-1=0

a = 4; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·4·(-1)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{97}}{2*4}=\frac{9-\sqrt{97}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{97}}{2*4}=\frac{9+\sqrt{97}}{8}
$