n^2+45n+144=0

Solution for n^2+45n+144=0 equation:

n^2+45n+144=0

a = 1; b = 45; c = +144;
Δ = b2-4ac
Δ = 452-4·1·144
Δ = 1449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{161}}{2*1}=\frac{-45-3\sqrt{161}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{161}}{2*1}=\frac{-45+3\sqrt{161}}{2}
$