10y^2=45

Solution for 10y^2=45 equation:

10y^2=45

We move all terms to the left:

10y^2-(45)=0

a = 10; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·10·(-45)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{2}}{2*10}=\frac{0-30\sqrt{2}}{20}
=-\frac{30\sqrt{2}}{20}
=-\frac{3\sqrt{2}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{2}}{2*10}=\frac{0+30\sqrt{2}}{20}
=\frac{30\sqrt{2}}{20}
=\frac{3\sqrt{2}}{2}
$