40-9y=y2

Solution for 40-9y=y2 equation:

40-9y=y2

We move all terms to the left:

40-9y-(y2)=0

We add all the numbers together, and all the variables

-1y^2-9y+40=0

a = -1; b = -9; c = +40;
Δ = b2-4ac
Δ = -92-4·(-1)·40
Δ = 241
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{-(-9)-\sqrt{241}}{2*-1}=\frac{9-\sqrt{241}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{241}}{2*-1}=\frac{9+\sqrt{241}}{-2}
$