490n^2-690=0

Solution for 490n^2-690=0 equation:

490n^2-690=0

a = 490; b = 0; c = -690;
Δ = b2-4ac
Δ = 02-4·490·(-690)
Δ = 1352400
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:

$\sqrt{\Delta}=\sqrt{1352400}=\sqrt{19600*69}=\sqrt{19600}*\sqrt{69}=140\sqrt{69}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-140\sqrt{69}}{2*490}=\frac{0-140\sqrt{69}}{980}
=-\frac{140\sqrt{69}}{980}
=-\frac{\sqrt{69}}{7}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+140\sqrt{69}}{2*490}=\frac{0+140\sqrt{69}}{980}
=\frac{140\sqrt{69}}{980}
=\frac{\sqrt{69}}{7}
$