1/5y-3=y

Solution for 1/5y-3=y equation:

1/5y-3=y

We move all terms to the left:

1/5y-3-(y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+1/5y-3=0

We multiply all the terms by the denominator


-1y*5y-3*5y+1=0

Wy multiply elements

-5y^2-15y+1=0

a = -5; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·(-5)·1
Δ = 245
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:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-7\sqrt{5}}{2*-5}=\frac{15-7\sqrt{5}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+7\sqrt{5}}{2*-5}=\frac{15+7\sqrt{5}}{-10}
$