5n^2+27n=57

Solution for 5n^2+27n=57 equation:

5n^2+27n=57

We move all terms to the left:

5n^2+27n-(57)=0

a = 5; b = 27; c = -57;
Δ = b2-4ac
Δ = 272-4·5·(-57)
Δ = 1869
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{-(27)-\sqrt{1869}}{2*5}=\frac{-27-\sqrt{1869}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{1869}}{2*5}=\frac{-27+\sqrt{1869}}{10}
$