6n^2+9n=105

Solution for 6n^2+9n=105 equation:

6n^2+9n=105

We move all terms to the left:

6n^2+9n-(105)=0

a = 6; b = 9; c = -105;
Δ = b2-4ac
Δ = 92-4·6·(-105)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-51}{2*6}=\frac{-60}{12}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+51}{2*6}=\frac{42}{12}
=3+1/2
$