3/5y=57y=

Solution for 3/5y=57y= equation:

3/5y=57y=

We move all terms to the left:

3/5y-(57y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

-57y+3/5y=0

We multiply all the terms by the denominator


-57y*5y+3=0

Wy multiply elements

-285y^2+3=0

a = -285; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-285)·3
Δ = 3420
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:

$\sqrt{\Delta}=\sqrt{3420}=\sqrt{36*95}=\sqrt{36}*\sqrt{95}=6\sqrt{95}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{95}}{2*-285}=\frac{0-6\sqrt{95}}{-570}
=-\frac{6\sqrt{95}}{-570}
=-\frac{\sqrt{95}}{-95}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{95}}{2*-285}=\frac{0+6\sqrt{95}}{-570}
=\frac{6\sqrt{95}}{-570}
=\frac{\sqrt{95}}{-95}
$