y-5=3-9(y2)

Solution for y-5=3-9(y2) equation:

y-5=3-9(y2)

We move all terms to the left:

y-5-(3-9(y2))=0

We add all the numbers together, and all the variables

-(-9y^2+3)+y-5=0

We get rid of parentheses

9y^2+y-3-5=0

We add all the numbers together, and all the variables

9y^2+y-8=0

a = 9; b = 1; c = -8;
Δ = b2-4ac
Δ = 12-4·9·(-8)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*9}=\frac{-18}{18}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*9}=\frac{16}{18}
=8/9
$