10y^2=18

Solution for 10y^2=18 equation:

10y^2=18

We move all terms to the left:

10y^2-(18)=0

a = 10; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·10·(-18)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*10}=\frac{0-12\sqrt{5}}{20}
=-\frac{12\sqrt{5}}{20}
=-\frac{3\sqrt{5}}{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*10}=\frac{0+12\sqrt{5}}{20}
=\frac{12\sqrt{5}}{20}
=\frac{3\sqrt{5}}{5}
$