5/9x=325x

Solution for 5/9x=325x equation:

5/9x=325x

We move all terms to the left:

5/9x-(325x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

-325x+5/9x=0

We multiply all the terms by the denominator


-325x*9x+5=0

Wy multiply elements

-2925x^2+5=0

a = -2925; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-2925)·5
Δ = 58500
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:

$\sqrt{\Delta}=\sqrt{58500}=\sqrt{900*65}=\sqrt{900}*\sqrt{65}=30\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{65}}{2*-2925}=\frac{0-30\sqrt{65}}{-5850}
=-\frac{30\sqrt{65}}{-5850}
=-\frac{\sqrt{65}}{-195}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{65}}{2*-2925}=\frac{0+30\sqrt{65}}{-5850}
=\frac{30\sqrt{65}}{-5850}
=\frac{\sqrt{65}}{-195}
$