49y^2-4=27

Solution for 49y^2-4=27 equation:

49y^2-4=27

We move all terms to the left:

49y^2-4-(27)=0

We add all the numbers together, and all the variables

49y^2-31=0

a = 49; b = 0; c = -31;
Δ = b2-4ac
Δ = 02-4·49·(-31)
Δ = 6076
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:

$\sqrt{\Delta}=\sqrt{6076}=\sqrt{196*31}=\sqrt{196}*\sqrt{31}=14\sqrt{31}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{31}}{2*49}=\frac{0-14\sqrt{31}}{98}
=-\frac{14\sqrt{31}}{98}
=-\frac{\sqrt{31}}{7}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{31}}{2*49}=\frac{0+14\sqrt{31}}{98}
=\frac{14\sqrt{31}}{98}
=\frac{\sqrt{31}}{7}
$