9n2+6n=3

Solution for 9n2+6n=3 equation:

9n^2+6n=3

We move all terms to the left:

9n^2+6n-(3)=0

a = 9; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·9·(-3)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12}{2*9}=\frac{-18}{18}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12}{2*9}=\frac{6}{18}
=1/3
$