1/2(2x-4)=1/9(18x+9)

Solution for 1/2(2x-4)=1/9(18x+9) equation:

1/2(2x-4)=1/9(18x+9)

We move all terms to the left:

1/2(2x-4)-(1/9(18x+9))=0


Domain of the equation: 2(2x-4)!=0

x∈R



Domain of the equation: 9(18x+9))!=0

x∈R


We calculate fractions


(9x1/(2(2x-4)*9(18x+9)))+(-2x2/(2(2x-4)*9(18x+9)))=0


We calculate terms in parentheses: +(9x1/(2(2x-4)*9(18x+9))), so:

9x1/(2(2x-4)*9(18x+9))

We multiply all the terms by the denominator


9x1

We add all the numbers together, and all the variables

9x

Back to the equation:

+(9x)



We calculate terms in parentheses: +(-2x2/(2(2x-4)*9(18x+9))), so:

-2x2/(2(2x-4)*9(18x+9))

We multiply all the terms by the denominator


-2x2

We add all the numbers together, and all the variables

-2x^2

Back to the equation:

+(-2x^2)


We get rid of parentheses

-2x^2+9x=0

a = -2; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-2)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-2}=\frac{-18}{-4}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-2}=\frac{0}{-4}
=0
$