32x-2=2/9x

Solution for 32x-2=2/9x equation:

32x-2=2/9x

We move all terms to the left:

32x-2-(2/9x)=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

32x-2/9x-2=0

We multiply all the terms by the denominator


32x*9x-2*9x-2=0

Wy multiply elements

288x^2-18x-2=0

a = 288; b = -18; c = -2;
Δ = b2-4ac
Δ = -182-4·288·(-2)
Δ = 2628
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:

$\sqrt{\Delta}=\sqrt{2628}=\sqrt{36*73}=\sqrt{36}*\sqrt{73}=6\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{73}}{2*288}=\frac{18-6\sqrt{73}}{576}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{73}}{2*288}=\frac{18+6\sqrt{73}}{576}
$