2n^2-7n-63=9

Solution for 2n^2-7n-63=9 equation:

2n^2-7n-63=9

We move all terms to the left:

2n^2-7n-63-(9)=0

We add all the numbers together, and all the variables

2n^2-7n-72=0

a = 2; b = -7; c = -72;
Δ = b2-4ac
Δ = -72-4·2·(-72)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-25}{2*2}=\frac{-18}{4}
=-4+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+25}{2*2}=\frac{32}{4}
=8
$