x+5/2x-1=32

Solution for x+5/2x-1=32 equation:

x+5/2x-1=32

We move all terms to the left:

x+5/2x-1-(32)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+5/2x-33=0

We multiply all the terms by the denominator


x*2x-33*2x+5=0

Wy multiply elements

2x^2-66x+5=0

a = 2; b = -66; c = +5;
Δ = b2-4ac
Δ = -662-4·2·5
Δ = 4316
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:

$\sqrt{\Delta}=\sqrt{4316}=\sqrt{4*1079}=\sqrt{4}*\sqrt{1079}=2\sqrt{1079}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1079}}{2*2}=\frac{66-2\sqrt{1079}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1079}}{2*2}=\frac{66+2\sqrt{1079}}{4}
$