(3/5)x=1/15

Solution for (3/5)x=1/15 equation:

(3/5)x=1/15

We move all terms to the left:

(3/5)x-(1/15)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/5)x-(+1/15)=0

We multiply parentheses

3x^2-(+1/15)=0

We get rid of parentheses

3x^2-1/15=0

We multiply all the terms by the denominator


3x^2*15-1=0

Wy multiply elements

45x^2-1=0

a = 45; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·45·(-1)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*45}=\frac{0-6\sqrt{5}}{90}
=-\frac{6\sqrt{5}}{90}
=-\frac{\sqrt{5}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*45}=\frac{0+6\sqrt{5}}{90}
=\frac{6\sqrt{5}}{90}
=\frac{\sqrt{5}}{15}
$