2x+28=5/2x

Solution for 2x+28=5/2x equation:

2x+28=5/2x

We move all terms to the left:

2x+28-(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

2x-(+5/2x)+28=0

We get rid of parentheses

2x-5/2x+28=0

We multiply all the terms by the denominator


2x*2x+28*2x-5=0

Wy multiply elements

4x^2+56x-5=0

a = 4; b = 56; c = -5;
Δ = b2-4ac
Δ = 562-4·4·(-5)
Δ = 3216
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:

$\sqrt{\Delta}=\sqrt{3216}=\sqrt{16*201}=\sqrt{16}*\sqrt{201}=4\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{201}}{2*4}=\frac{-56-4\sqrt{201}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{201}}{2*4}=\frac{-56+4\sqrt{201}}{8}
$