3/5x=9x=

Solution for 3/5x=9x= equation:

3/5x=9x=

We move all terms to the left:

3/5x-(9x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-9x+3/5x=0

We multiply all the terms by the denominator


-9x*5x+3=0

Wy multiply elements

-45x^2+3=0

a = -45; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-45)·3
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{15}}{2*-45}=\frac{0-6\sqrt{15}}{-90}
=-\frac{6\sqrt{15}}{-90}
=-\frac{\sqrt{15}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{15}}{2*-45}=\frac{0+6\sqrt{15}}{-90}
=\frac{6\sqrt{15}}{-90}
=\frac{\sqrt{15}}{-15}
$