5y-16/3y=-1

Solution for 5y-16/3y=-1 equation:

5y-16/3y=-1

We move all terms to the left:

5y-16/3y-(-1)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

5y-16/3y+1=0

We multiply all the terms by the denominator


5y*3y+1*3y-16=0

Wy multiply elements

15y^2+3y-16=0

a = 15; b = 3; c = -16;
Δ = b2-4ac
Δ = 32-4·15·(-16)
Δ = 969
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{-(3)-\sqrt{969}}{2*15}=\frac{-3-\sqrt{969}}{30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{969}}{2*15}=\frac{-3+\sqrt{969}}{30}
$