0=4x-5/2x-1

Solution for 0=4x-5/2x-1 equation:

0=4x-5/2x-1

We move all terms to the left:

0-(4x-5/2x-1)=0


Domain of the equation: 2x-1)!=0

x∈R


We add all the numbers together, and all the variables

-(4x-5/2x-1)=0

We get rid of parentheses

-4x+5/2x+1=0

We multiply all the terms by the denominator


-4x*2x+1*2x+5=0

Wy multiply elements

-8x^2+2x+5=0

a = -8; b = 2; c = +5;
Δ = b2-4ac
Δ = 22-4·(-8)·5
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{41}}{2*-8}=\frac{-2-2\sqrt{41}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{41}}{2*-8}=\frac{-2+2\sqrt{41}}{-16}
$