9/2x+2x=21

Solution for 9/2x+2x=21 equation:

9/2x+2x=21

We move all terms to the left:

9/2x+2x-(21)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+9/2x-21=0

We multiply all the terms by the denominator


2x*2x-21*2x+9=0

Wy multiply elements

4x^2-42x+9=0

a = 4; b = -42; c = +9;
Δ = b2-4ac
Δ = -422-4·4·9
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-18\sqrt{5}}{2*4}=\frac{42-18\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+18\sqrt{5}}{2*4}=\frac{42+18\sqrt{5}}{8}
$