1/32x+9=2/3x

Solution for 1/32x+9=2/3x equation:

1/32x+9=2/3x

We move all terms to the left:

1/32x+9-(2/3x)=0


Domain of the equation: 32x!=0

x!=0/32

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/32x-(+2/3x)+9=0

We get rid of parentheses

1/32x-2/3x+9=0

We calculate fractions


3x/96x^2+(-64x)/96x^2+9=0

We multiply all the terms by the denominator


3x+(-64x)+9*96x^2=0

Wy multiply elements

864x^2+3x+(-64x)=0

We get rid of parentheses

864x^2+3x-64x=0

We add all the numbers together, and all the variables

864x^2-61x=0

a = 864; b = -61; c = 0;
Δ = b2-4ac
Δ = -612-4·864·0
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-61}{2*864}=\frac{0}{1728}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+61}{2*864}=\frac{122}{1728}
=61/864
$