5n^2+6n=171

Solution for 5n^2+6n=171 equation:

5n^2+6n=171

We move all terms to the left:

5n^2+6n-(171)=0

a = 5; b = 6; c = -171;
Δ = b2-4ac
Δ = 62-4·5·(-171)
Δ = 3456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-24\sqrt{6}}{2*5}=\frac{-6-24\sqrt{6}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+24\sqrt{6}}{2*5}=\frac{-6+24\sqrt{6}}{10}
$