6n^2+48n-54=0

Solution for 6n^2+48n-54=0 equation:

6n^2+48n-54=0

a = 6; b = 48; c = -54;
Δ = b2-4ac
Δ = 482-4·6·(-54)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-60}{2*6}=\frac{-108}{12}
=-9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+60}{2*6}=\frac{12}{12}
=1
$