45+20y-y^2=0

Solution for 45+20y-y^2=0 equation:

45+20y-y^2=0

We add all the numbers together, and all the variables

-1y^2+20y+45=0

a = -1; b = 20; c = +45;
Δ = b2-4ac
Δ = 202-4·(-1)·45
Δ = 580
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{145}}{2*-1}=\frac{-20-2\sqrt{145}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{145}}{2*-1}=\frac{-20+2\sqrt{145}}{-2}
$