y2-18y-45=0

Solution for y2-18y-45=0 equation:

y2-18y-45=0

We add all the numbers together, and all the variables

y^2-18y-45=0

a = 1; b = -18; c = -45;
Δ = b2-4ac
Δ = -182-4·1·(-45)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{14}}{2*1}=\frac{18-6\sqrt{14}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{14}}{2*1}=\frac{18+6\sqrt{14}}{2}
$