(2x+10)=5/2x

Solution for (2x+10)=5/2x equation:

(2x+10)=5/2x

We move all terms to the left:

(2x+10)-(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+10)-(+5/2x)=0

We get rid of parentheses

2x-5/2x+10=0

We multiply all the terms by the denominator


2x*2x+10*2x-5=0

Wy multiply elements

4x^2+20x-5=0

a = 4; b = 20; c = -5;
Δ = b2-4ac
Δ = 202-4·4·(-5)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{30}}{2*4}=\frac{-20-4\sqrt{30}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{30}}{2*4}=\frac{-20+4\sqrt{30}}{8}
$