5s^2-14-240=0

Solution for 5s^2-14-240=0 equation:

5s^2-14-240=0

We add all the numbers together, and all the variables

5s^2-254=0

a = 5; b = 0; c = -254;
Δ = b2-4ac
Δ = 02-4·5·(-254)
Δ = 5080
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5080}=\sqrt{4*1270}=\sqrt{4}*\sqrt{1270}=2\sqrt{1270}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{1270}}{2*5}=\frac{0-2\sqrt{1270}}{10}
=-\frac{2\sqrt{1270}}{10}
=-\frac{\sqrt{1270}}{5}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{1270}}{2*5}=\frac{0+2\sqrt{1270}}{10}
=\frac{2\sqrt{1270}}{10}
=\frac{\sqrt{1270}}{5}
$