3n2-n-14=-4

Solution for 3n2-n-14=-4 equation:

3n^2-n-14=-4

We move all terms to the left:

3n^2-n-14-(-4)=0

We add all the numbers together, and all the variables

3n^2-1n-10=0

a = 3; b = -1; c = -10;
Δ = b2-4ac
Δ = -12-4·3·(-10)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*3}=\frac{-10}{6}
=-1+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*3}=\frac{12}{6}
=2
$