5n2=7

Solution for 5n2=7 equation:

5n^2=7

We move all terms to the left:

5n^2-(7)=0

a = 5; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·5·(-7)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{35}}{2*5}=\frac{0-2\sqrt{35}}{10}
=-\frac{2\sqrt{35}}{10}
=-\frac{\sqrt{35}}{5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{35}}{2*5}=\frac{0+2\sqrt{35}}{10}
=\frac{2\sqrt{35}}{10}
=\frac{\sqrt{35}}{5}
$