2n(n-4)+3n=37

Solution for 2n(n-4)+3n=37 equation:

2n(n-4)+3n=37

We move all terms to the left:

2n(n-4)+3n-(37)=0

We add all the numbers together, and all the variables

3n+2n(n-4)-37=0

We multiply parentheses

2n^2+3n-8n-37=0

We add all the numbers together, and all the variables

2n^2-5n-37=0

a = 2; b = -5; c = -37;
Δ = b2-4ac
Δ = -52-4·2·(-37)
Δ = 321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{321}}{2*2}=\frac{5-\sqrt{321}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{321}}{2*2}=\frac{5+\sqrt{321}}{4}
$