30+2/9x=100x

Solution for 30+2/9x=100x equation:

30+2/9x=100x

We move all terms to the left:

30+2/9x-(100x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

-100x+2/9x+30=0

We multiply all the terms by the denominator


-100x*9x+30*9x+2=0

Wy multiply elements

-900x^2+270x+2=0

a = -900; b = 270; c = +2;
Δ = b2-4ac
Δ = 2702-4·(-900)·2
Δ = 80100
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:

$\sqrt{\Delta}=\sqrt{80100}=\sqrt{900*89}=\sqrt{900}*\sqrt{89}=30\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(270)-30\sqrt{89}}{2*-900}=\frac{-270-30\sqrt{89}}{-1800}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(270)+30\sqrt{89}}{2*-900}=\frac{-270+30\sqrt{89}}{-1800}
$