4x-2=5/2x

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

4x-2=5/2x

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4x-5/2x-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

8x^2-4x-5=0

a = 8; b = -4; c = -5;
Δ = b2-4ac
Δ = -42-4·8·(-5)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{11}}{2*8}=\frac{4-4\sqrt{11}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{11}}{2*8}=\frac{4+4\sqrt{11}}{16}
$