5n^2-8=57

Solution for 5n^2-8=57 equation:

5n^2-8=57

We move all terms to the left:

5n^2-8-(57)=0

We add all the numbers together, and all the variables

5n^2-65=0

a = 5; b = 0; c = -65;
Δ = b2-4ac
Δ = 02-4·5·(-65)
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{13}}{2*5}=\frac{0-10\sqrt{13}}{10}
=-\frac{10\sqrt{13}}{10}
=-\sqrt{13}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{13}}{2*5}=\frac{0+10\sqrt{13}}{10}
=\frac{10\sqrt{13}}{10}
=\sqrt{13}
$