5n(n-3)=7+3n

Solution for 5n(n-3)=7+3n equation:

5n(n-3)=7+3n

We move all terms to the left:

5n(n-3)-(7+3n)=0

We add all the numbers together, and all the variables

5n(n-3)-(3n+7)=0

We multiply parentheses

5n^2-15n-(3n+7)=0

We get rid of parentheses

5n^2-15n-3n-7=0

We add all the numbers together, and all the variables

5n^2-18n-7=0

a = 5; b = -18; c = -7;
Δ = b2-4ac
Δ = -182-4·5·(-7)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{29}}{2*5}=\frac{18-4\sqrt{29}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{29}}{2*5}=\frac{18+4\sqrt{29}}{10}
$