3n^2-n-30=0

Solution for 3n^2-n-30=0 equation:

3n^2-n-30=0

We add all the numbers together, and all the variables

3n^2-1n-30=0

a = 3; b = -1; c = -30;
Δ = b2-4ac
Δ = -12-4·3·(-30)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-19}{2*3}=\frac{-18}{6}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+19}{2*3}=\frac{20}{6}
=3+1/3
$