6y^2-6=45

Solution for 6y^2-6=45 equation:

6y^2-6=45

We move all terms to the left:

6y^2-6-(45)=0

We add all the numbers together, and all the variables

6y^2-51=0

a = 6; b = 0; c = -51;
Δ = b2-4ac
Δ = 02-4·6·(-51)
Δ = 1224
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:

$\sqrt{\Delta}=\sqrt{1224}=\sqrt{36*34}=\sqrt{36}*\sqrt{34}=6\sqrt{34}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{34}}{2*6}=\frac{0-6\sqrt{34}}{12}
=-\frac{6\sqrt{34}}{12}
=-\frac{\sqrt{34}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{34}}{2*6}=\frac{0+6\sqrt{34}}{12}
=\frac{6\sqrt{34}}{12}
=\frac{\sqrt{34}}{2}
$