10y2=2

Solution for 10y2=2 equation:

10y^2=2

We move all terms to the left:

10y^2-(2)=0

a = 10; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·10·(-2)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*10}=\frac{0-4\sqrt{5}}{20}
=-\frac{4\sqrt{5}}{20}
=-\frac{\sqrt{5}}{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*10}=\frac{0+4\sqrt{5}}{20}
=\frac{4\sqrt{5}}{20}
=\frac{\sqrt{5}}{5}
$