(3/5)y=9/25

Solution for (3/5)y=9/25 equation:

(3/5)y=9/25

We move all terms to the left:

(3/5)y-(9/25)=0


Domain of the equation: 5)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+3/5)y-(+9/25)=0

We multiply parentheses

3y^2-(+9/25)=0

We get rid of parentheses

3y^2-9/25=0

We multiply all the terms by the denominator


3y^2*25-9=0

Wy multiply elements

75y^2-9=0

a = 75; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·75·(-9)
Δ = 2700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{3}}{2*75}=\frac{0-30\sqrt{3}}{150}
=-\frac{30\sqrt{3}}{150}
=-\frac{\sqrt{3}}{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{3}}{2*75}=\frac{0+30\sqrt{3}}{150}
=\frac{30\sqrt{3}}{150}
=\frac{\sqrt{3}}{5}
$