5n^2-27n=-28

Solution for 5n^2-27n=-28 equation:

5n^2-27n=-28

We move all terms to the left:

5n^2-27n-(-28)=0

We add all the numbers together, and all the variables

5n^2-27n+28=0

a = 5; b = -27; c = +28;
Δ = b2-4ac
Δ = -272-4·5·28
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-13}{2*5}=\frac{14}{10}
=1+2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+13}{2*5}=\frac{40}{10}
=4
$