10y^2-7=2

Solution for 10y^2-7=2 equation:

10y^2-7=2

We move all terms to the left:

10y^2-7-(2)=0

We add all the numbers together, and all the variables

10y^2-9=0

a = 10; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·10·(-9)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10}}{2*10}=\frac{0-6\sqrt{10}}{20}
=-\frac{6\sqrt{10}}{20}
=-\frac{3\sqrt{10}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*10}=\frac{0+6\sqrt{10}}{20}
=\frac{6\sqrt{10}}{20}
=\frac{3\sqrt{10}}{10}
$