0.15y(y-0.2)=2-0.5+0.5y

Solution for 0.15y(y-0.2)=2-0.5+0.5y equation:

0.15y(y-0.2)=2-0.5+0.5y

We move all terms to the left:

0.15y(y-0.2)-(2-0.5+0.5y)=0

We add all the numbers together, and all the variables

0.15y(y-0.2)-(0.5y+1.5)=0

We multiply parentheses

0y^2-0y-(0.5y+1.5)=0

We get rid of parentheses

0y^2-0y-0.5y-1.5=0

We add all the numbers together, and all the variables

y^2-1.5y-1.5=0

a = 1; b = -1.5; c = -1.5;
Δ = b2-4ac
Δ = -1.52-4·1·(-1.5)
Δ = 8.25
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{-(-1.5)-\sqrt{8.25}}{2*1}=\frac{1.5-\sqrt{8.25}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{8.25}}{2*1}=\frac{1.5+\sqrt{8.25}}{2}
$