2n^2-45n-252=0

Solution for 2n^2-45n-252=0 equation:

2n^2-45n-252=0

a = 2; b = -45; c = -252;
Δ = b2-4ac
Δ = -452-4·2·(-252)
Δ = 4041
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:

$\sqrt{\Delta}=\sqrt{4041}=\sqrt{9*449}=\sqrt{9}*\sqrt{449}=3\sqrt{449}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{449}}{2*2}=\frac{45-3\sqrt{449}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{449}}{2*2}=\frac{45+3\sqrt{449}}{4}
$