84y^2-5=0

Solution for 84y^2-5=0 equation:

84y^2-5=0

a = 84; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·84·(-5)
Δ = 1680
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{105}}{2*84}=\frac{0-4\sqrt{105}}{168}
=-\frac{4\sqrt{105}}{168}
=-\frac{\sqrt{105}}{42}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{105}}{2*84}=\frac{0+4\sqrt{105}}{168}
=\frac{4\sqrt{105}}{168}
=\frac{\sqrt{105}}{42}
$