18/6x+9-2/3=4/2x+3

Solution for 18/6x+9-2/3=4/2x+3 equation:

18/6x+9-2/3=4/2x+3

We move all terms to the left:

18/6x+9-2/3-(4/2x+3)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

18/6x-4/2x-3+9-2/3=0

We calculate fractions


(-48x^2)/108x^2+324x/108x^2+(-216x)/108x^2-3+9=0

We add all the numbers together, and all the variables

(-48x^2)/108x^2+324x/108x^2+(-216x)/108x^2+6=0

We multiply all the terms by the denominator


(-48x^2)+324x+(-216x)+6*108x^2=0

Wy multiply elements

(-48x^2)+648x^2+324x+(-216x)=0

We get rid of parentheses

-48x^2+648x^2+324x-216x=0

We add all the numbers together, and all the variables

600x^2+108x=0

a = 600; b = 108; c = 0;
Δ = b2-4ac
Δ = 1082-4·600·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108}{2*600}=\frac{-216}{1200}
=-9/50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108}{2*600}=\frac{0}{1200}
=0
$