y^2-14-240=0

Solution for y^2-14-240=0 equation:

y^2-14-240=0

We add all the numbers together, and all the variables

y^2-254=0

a = 1; b = 0; c = -254;
Δ = b2-4ac
Δ = 02-4·1·(-254)
Δ = 1016
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:

$\sqrt{\Delta}=\sqrt{1016}=\sqrt{4*254}=\sqrt{4}*\sqrt{254}=2\sqrt{254}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{254}}{2*1}=\frac{0-2\sqrt{254}}{2}
=-\frac{2\sqrt{254}}{2}
=-\sqrt{254}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{254}}{2*1}=\frac{0+2\sqrt{254}}{2}
=\frac{2\sqrt{254}}{2}
=\sqrt{254}
$