n^2+5n=0.2677

Solution for n^2+5n=0.2677 equation:

n^2+5n=0.2677

We move all terms to the left:

n^2+5n-(0.2677)=0

We add all the numbers together, and all the variables

n^2+5n-0.2677=0

a = 1; b = 5; c = -0.2677;
Δ = b2-4ac
Δ = 52-4·1·(-0.2677)
Δ = 26.0708
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{26.0708}}{2*1}=\frac{-5-\sqrt{26.0708}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{26.0708}}{2*1}=\frac{-5+\sqrt{26.0708}}{2}
$