9n2-18n+3=-5

Solution for 9n2-18n+3=-5 equation:

9n^2-18n+3=-5

We move all terms to the left:

9n^2-18n+3-(-5)=0

We add all the numbers together, and all the variables

9n^2-18n+8=0

a = 9; b = -18; c = +8;
Δ = b2-4ac
Δ = -182-4·9·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6}{2*9}=\frac{12}{18}
=2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6}{2*9}=\frac{24}{18}
=1+1/3
$