5=15y-y^2

Solution for 5=15y-y^2 equation:

5=15y-y^2

We move all terms to the left:

5-(15y-y^2)=0

We get rid of parentheses

y^2-15y+5=0

a = 1; b = -15; c = +5;
Δ = b2-4ac
Δ = -152-4·1·5
Δ = 205
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{-(-15)-\sqrt{205}}{2*1}=\frac{15-\sqrt{205}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{205}}{2*1}=\frac{15+\sqrt{205}}{2}
$