0.18y(y-5)+0.02y=0.10y=0.5

Solution for 0.18y(y-5)+0.02y=0.10y=0.5 equation:

0.18y(y-5)+0.02y=0.10y=0.5

We move all terms to the left:

0.18y(y-5)+0.02y-(0.10y)=0

We add all the numbers together, and all the variables

0.18y(y-5)+0.02y-(+0.10y)=0

We add all the numbers together, and all the variables

0.02y+0.18y(y-5)-(+0.10y)=0

We multiply parentheses

0y^2+0.02y+0y-(+0.10y)=0

We get rid of parentheses

0y^2+0.02y+0y-0.10y=0

We add all the numbers together, and all the variables

y^2+0.92y=0

a = 1; b = 0.92; c = 0;
Δ = b2-4ac
Δ = 0.922-4·1·0
Δ = 0.8464
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{-(0.92)-\sqrt{0.8464}}{2*1}=\frac{-0.92-\sqrt{0.8464}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.92)+\sqrt{0.8464}}{2*1}=\frac{-0.92+\sqrt{0.8464}}{2}
$