5n^2-4=71

Solution for 5n^2-4=71 equation:

5n^2-4=71

We move all terms to the left:

5n^2-4-(71)=0

We add all the numbers together, and all the variables

5n^2-75=0

a = 5; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·5·(-75)
Δ = 1500
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:

$\sqrt{\Delta}=\sqrt{1500}=\sqrt{100*15}=\sqrt{100}*\sqrt{15}=10\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{15}}{2*5}=\frac{0-10\sqrt{15}}{10}
=-\frac{10\sqrt{15}}{10}
=-\sqrt{15}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{15}}{2*5}=\frac{0+10\sqrt{15}}{10}
=\frac{10\sqrt{15}}{10}
=\sqrt{15}
$