5n+2=n2

Solution for 5n+2=n2 equation:

5n+2=n2

We move all terms to the left:

5n+2-(n2)=0

We add all the numbers together, and all the variables

-1n^2+5n+2=0

a = -1; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·(-1)·2
Δ = 33
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{33}}{2*-1}=\frac{-5-\sqrt{33}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{33}}{2*-1}=\frac{-5+\sqrt{33}}{-2}
$