y(0.5y+0.5)=15

Solution for y(0.5y+0.5)=15 equation:

y(0.5y+0.5)=15

We move all terms to the left:

y(0.5y+0.5)-(15)=0

We multiply parentheses

0y^2+0.5y-15=0

We add all the numbers together, and all the variables

y^2+0.5y-15=0

a = 1; b = 0.5; c = -15;
Δ = b2-4ac
Δ = 0.52-4·1·(-15)
Δ = 60.25
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{-(0.5)-\sqrt{60.25}}{2*1}=\frac{-0.5-\sqrt{60.25}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{60.25}}{2*1}=\frac{-0.5+\sqrt{60.25}}{2}
$