120x^2-250+2=0

Solution for 120x^2-250+2=0 equation:

120x^2-250+2=0

We add all the numbers together, and all the variables

120x^2-248=0

a = 120; b = 0; c = -248;
Δ = b2-4ac
Δ = 02-4·120·(-248)
Δ = 119040
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{119040}=\sqrt{256*465}=\sqrt{256}*\sqrt{465}=16\sqrt{465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{465}}{2*120}=\frac{0-16\sqrt{465}}{240}
=-\frac{16\sqrt{465}}{240}
=-\frac{\sqrt{465}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{465}}{2*120}=\frac{0+16\sqrt{465}}{240}
=\frac{16\sqrt{465}}{240}
=\frac{\sqrt{465}}{15}
$