5+2x=21/2x

Solution for 5+2x=21/2x equation:

5+2x=21/2x

We move all terms to the left:

5+2x-(21/2x)=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-(+21/2x)+5=0

We get rid of parentheses

2x-21/2x+5=0

We multiply all the terms by the denominator


2x*2x+5*2x-21=0

Wy multiply elements

4x^2+10x-21=0

a = 4; b = 10; c = -21;
Δ = b2-4ac
Δ = 102-4·4·(-21)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{109}}{2*4}=\frac{-10-2\sqrt{109}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{109}}{2*4}=\frac{-10+2\sqrt{109}}{8}
$