5n^2+20n+2=11n

Solution for 5n^2+20n+2=11n equation:

5n^2+20n+2=11n

We move all terms to the left:

5n^2+20n+2-(11n)=0

We add all the numbers together, and all the variables

5n^2+9n+2=0

a = 5; b = 9; c = +2;
Δ = b2-4ac
Δ = 92-4·5·2
Δ = 41
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{-(9)-\sqrt{41}}{2*5}=\frac{-9-\sqrt{41}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{41}}{2*5}=\frac{-9+\sqrt{41}}{10}
$