3n+1.55=n*n

Solution for 3n+1.55=n*n equation:

3n+1.55=n*n

We move all terms to the left:

3n+1.55-(n*n)=0

We add all the numbers together, and all the variables

3n-(+n*n)+1.55=0

We get rid of parentheses

3n-n*n+1.55=0

Wy multiply elements

-1n^2+3n+1.55=0

a = -1; b = 3; c = +1.55;
Δ = b2-4ac
Δ = 32-4·(-1)·1.55
Δ = 15.2
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{-(3)-\sqrt{15.2}}{2*-1}=\frac{-3-\sqrt{15.2}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{15.2}}{2*-1}=\frac{-3+\sqrt{15.2}}{-2}
$