(1+3y)y=80

Solution for (1+3y)y=80 equation:

(1+3y)y=80

We move all terms to the left:

(1+3y)y-(80)=0

We add all the numbers together, and all the variables

(3y+1)y-80=0

We multiply parentheses

3y^2+y-80=0

a = 3; b = 1; c = -80;
Δ = b2-4ac
Δ = 12-4·3·(-80)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-31}{2*3}=\frac{-32}{6}
=-5+1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+31}{2*3}=\frac{30}{6}
=5
$