3n2-14=-9n

Solution for 3n2-14=-9n equation:

3n^2-14=-9n

We move all terms to the left:

3n^2-14-(-9n)=0

We get rid of parentheses

3n^2+9n-14=0

a = 3; b = 9; c = -14;
Δ = b2-4ac
Δ = 92-4·3·(-14)
Δ = 249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{249}}{2*3}=\frac{-9-\sqrt{249}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{249}}{2*3}=\frac{-9+\sqrt{249}}{6}
$