2/9x+9/4=2+3/2x

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

2/9x+9/4=2+3/2x

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


324x^2/288x^2+64x/288x^2+(-432x)/288x^2-2=0

We multiply all the terms by the denominator


324x^2+64x+(-432x)-2*288x^2=0

Wy multiply elements

324x^2-576x^2+64x+(-432x)=0

We get rid of parentheses

324x^2-576x^2+64x-432x=0

We add all the numbers together, and all the variables

-252x^2-368x=0

a = -252; b = -368; c = 0;
Δ = b2-4ac
Δ = -3682-4·(-252)·0
Δ = 135424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{135424}=368$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-368)-368}{2*-252}=\frac{0}{-504}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-368)+368}{2*-252}=\frac{736}{-504}
=-1+29/63
$