n(5n-3)=36

Solution for n(5n-3)=36 equation:

n(5n-3)=36

We move all terms to the left:

n(5n-3)-(36)=0

We multiply parentheses

5n^2-3n-36=0

a = 5; b = -3; c = -36;
Δ = b2-4ac
Δ = -32-4·5·(-36)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-27}{2*5}=\frac{-24}{10}
=-2+2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+27}{2*5}=\frac{30}{10}
=3
$