5y^2-2=47

Solution for 5y^2-2=47 equation:

5y^2-2=47

We move all terms to the left:

5y^2-2-(47)=0

We add all the numbers together, and all the variables

5y^2-49=0

a = 5; b = 0; c = -49;
Δ = b2-4ac
Δ = 02-4·5·(-49)
Δ = 980
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:

$\sqrt{\Delta}=\sqrt{980}=\sqrt{196*5}=\sqrt{196}*\sqrt{5}=14\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{5}}{2*5}=\frac{0-14\sqrt{5}}{10}
=-\frac{14\sqrt{5}}{10}
=-\frac{7\sqrt{5}}{5}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{5}}{2*5}=\frac{0+14\sqrt{5}}{10}
=\frac{14\sqrt{5}}{10}
=\frac{7\sqrt{5}}{5}
$