5/2x=2x+8

Solution for 5/2x=2x+8 equation:

5/2x=2x+8

We move all terms to the left:

5/2x-(2x+8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5/2x-2x-8=0

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2-16x+5=0

a = -4; b = -16; c = +5;
Δ = b2-4ac
Δ = -162-4·(-4)·5
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{21}}{2*-4}=\frac{16-4\sqrt{21}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{21}}{2*-4}=\frac{16+4\sqrt{21}}{-8}
$