5n^2-4=171

Solution for 5n^2-4=171 equation:

5n^2-4=171

We move all terms to the left:

5n^2-4-(171)=0

We add all the numbers together, and all the variables

5n^2-175=0

a = 5; b = 0; c = -175;
Δ = b2-4ac
Δ = 02-4·5·(-175)
Δ = 3500
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:

$\sqrt{\Delta}=\sqrt{3500}=\sqrt{100*35}=\sqrt{100}*\sqrt{35}=10\sqrt{35}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{35}}{2*5}=\frac{0-10\sqrt{35}}{10}
=-\frac{10\sqrt{35}}{10}
=-\sqrt{35}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{35}}{2*5}=\frac{0+10\sqrt{35}}{10}
=\frac{10\sqrt{35}}{10}
=\sqrt{35}
$