5/2x-1=2x+4

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

5/2x-1=2x+4

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2-8x-2x+5=0

We add all the numbers together, and all the variables

-4x^2-10x+5=0

a = -4; b = -10; c = +5;
Δ = b2-4ac
Δ = -102-4·(-4)·5
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{5}}{2*-4}=\frac{10-6\sqrt{5}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{5}}{2*-4}=\frac{10+6\sqrt{5}}{-8}
$