3*(y-15)+(y*y)=80

Solution for 3*(y-15)+(y*y)=80 equation:

3(y-15)+(y*y)=80

We move all terms to the left:

3(y-15)+(y*y)-(80)=0

We add all the numbers together, and all the variables

3(y-15)+(+y*y)-80=0

We multiply parentheses

3y+(+y*y)-45-80=0

We get rid of parentheses

3y+y*y-45-80=0

We add all the numbers together, and all the variables

3y+y*y-125=0

Wy multiply elements

y^2+3y-125=0

a = 1; b = 3; c = -125;
Δ = b2-4ac
Δ = 32-4·1·(-125)
Δ = 509
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{509}}{2*1}=\frac{-3-\sqrt{509}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{509}}{2*1}=\frac{-3+\sqrt{509}}{2}
$