45y-y2-180=0

Solution for 45y-y2-180=0 equation:

45y-y2-180=0

We add all the numbers together, and all the variables

-1y^2+45y-180=0

a = -1; b = 45; c = -180;
Δ = b2-4ac
Δ = 452-4·(-1)·(-180)
Δ = 1305
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:

$\sqrt{\Delta}=\sqrt{1305}=\sqrt{9*145}=\sqrt{9}*\sqrt{145}=3\sqrt{145}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{145}}{2*-1}=\frac{-45-3\sqrt{145}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{145}}{2*-1}=\frac{-45+3\sqrt{145}}{-2}
$