30n^2+57n-27=9

Solution for 30n^2+57n-27=9 equation:

30n^2+57n-27=9

We move all terms to the left:

30n^2+57n-27-(9)=0

We add all the numbers together, and all the variables

30n^2+57n-36=0

a = 30; b = 57; c = -36;
Δ = b2-4ac
Δ = 572-4·30·(-36)
Δ = 7569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7569}=87$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-87}{2*30}=\frac{-144}{60}
=-2+2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+87}{2*30}=\frac{30}{60}
=1/2
$