9n(2n-3)=29

Solution for 9n(2n-3)=29 equation:

9n(2n-3)=29

We move all terms to the left:

9n(2n-3)-(29)=0

We multiply parentheses

18n^2-27n-29=0

a = 18; b = -27; c = -29;
Δ = b2-4ac
Δ = -272-4·18·(-29)
Δ = 2817
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2817}=\sqrt{9*313}=\sqrt{9}*\sqrt{313}=3\sqrt{313}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{313}}{2*18}=\frac{27-3\sqrt{313}}{36}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{313}}{2*18}=\frac{27+3\sqrt{313}}{36}
$