3x+6=(21+3)/2x

Solution for 3x+6=(21+3)/2x equation:

3x+6=(21+3)/2x

We move all terms to the left:

3x+6-((21+3)/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

3x-(24/2x)+6=0

We get rid of parentheses

3x-24/2x+6=0

We multiply all the terms by the denominator


3x*2x+6*2x-24=0

Wy multiply elements

6x^2+12x-24=0

a = 6; b = 12; c = -24;
Δ = b2-4ac
Δ = 122-4·6·(-24)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{5}}{2*6}=\frac{-12-12\sqrt{5}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{5}}{2*6}=\frac{-12+12\sqrt{5}}{12}
$