2x+60=1/2x

Solution for 2x+60=1/2x equation:

2x+60=1/2x

We move all terms to the left:

2x+60-(1/2x)=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-(+1/2x)+60=0

We get rid of parentheses

2x-1/2x+60=0

We multiply all the terms by the denominator


2x*2x+60*2x-1=0

Wy multiply elements

4x^2+120x-1=0

a = 4; b = 120; c = -1;
Δ = b2-4ac
Δ = 1202-4·4·(-1)
Δ = 14416
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:

$\sqrt{\Delta}=\sqrt{14416}=\sqrt{16*901}=\sqrt{16}*\sqrt{901}=4\sqrt{901}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-4\sqrt{901}}{2*4}=\frac{-120-4\sqrt{901}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+4\sqrt{901}}{2*4}=\frac{-120+4\sqrt{901}}{8}
$