63n^2+33n-120=0

Solution for 63n^2+33n-120=0 equation:

63n^2+33n-120=0

a = 63; b = 33; c = -120;
Δ = b2-4ac
Δ = 332-4·63·(-120)
Δ = 31329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{31329}=177$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-177}{2*63}=\frac{-210}{126}
=-1+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+177}{2*63}=\frac{144}{126}
=1+1/7
$