9y+y=-9y2

Solution for 9y+y=-9y2 equation:

9y+y=-9y^2

We move all terms to the left:

9y+y-(-9y^2)=0

We add all the numbers together, and all the variables

-(-9y^2)+10y=0

We get rid of parentheses

9y^2+10y=0

a = 9; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·9·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*9}=\frac{-20}{18}
=-1+1/9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*9}=\frac{0}{18}
=0
$