y*(y-0.5)=5

Solution for y*(y-0.5)=5 equation:

y(y-0.5)=5

We move all terms to the left:

y(y-0.5)-(5)=0

We multiply parentheses

y^2-0.5y-5=0

a = 1; b = -0.5; c = -5;
Δ = b2-4ac
Δ = -0.52-4·1·(-5)
Δ = 20.25
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{20.25}}{2*1}=\frac{0.5-\sqrt{20.25}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{20.25}}{2*1}=\frac{0.5+\sqrt{20.25}}{2}
$