3y+1/5y=7

Solution for 3y+1/5y=7 equation:

3y+1/5y=7

We move all terms to the left:

3y+1/5y-(7)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We multiply all the terms by the denominator


3y*5y-7*5y+1=0

Wy multiply elements

15y^2-35y+1=0

a = 15; b = -35; c = +1;
Δ = b2-4ac
Δ = -352-4·15·1
Δ = 1165
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-\sqrt{1165}}{2*15}=\frac{35-\sqrt{1165}}{30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1165}}{2*15}=\frac{35+\sqrt{1165}}{30}
$