7y^2=10

Solution for 7y^2=10 equation:

7y^2=10

We move all terms to the left:

7y^2-(10)=0

a = 7; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·7·(-10)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{70}}{2*7}=\frac{0-2\sqrt{70}}{14}
=-\frac{2\sqrt{70}}{14}
=-\frac{\sqrt{70}}{7}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{70}}{2*7}=\frac{0+2\sqrt{70}}{14}
=\frac{2\sqrt{70}}{14}
=\frac{\sqrt{70}}{7}
$