3.6=9(y+0.1)y=

Solution for 3.6=9(y+0.1)y= equation:

3.6=9(y+0.1)y=

We move all terms to the left:

3.6-(9(y+0.1)y)=0


We calculate terms in parentheses: -(9(y+0.1)y), so:

9(y+0.1)y

We multiply parentheses

9y^2+0.9y

Back to the equation:

-(9y^2+0.9y)


We get rid of parentheses

-9y^2-0.9y+3.6=0

a = -9; b = -0.9; c = +3.6;
Δ = b2-4ac
Δ = -0.92-4·(-9)·3.6
Δ = 130.41
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{-(-0.9)-\sqrt{130.41}}{2*-9}=\frac{0.9-\sqrt{130.41}}{-18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.9)+\sqrt{130.41}}{2*-9}=\frac{0.9+\sqrt{130.41}}{-18}
$