10x^2-2=308

Solution for 10x^2-2=308 equation:

10x^2-2=308

We move all terms to the left:

10x^2-2-(308)=0

We add all the numbers together, and all the variables

10x^2-310=0

a = 10; b = 0; c = -310;
Δ = b2-4ac
Δ = 02-4·10·(-310)
Δ = 12400
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:

$\sqrt{\Delta}=\sqrt{12400}=\sqrt{400*31}=\sqrt{400}*\sqrt{31}=20\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{31}}{2*10}=\frac{0-20\sqrt{31}}{20}
=-\frac{20\sqrt{31}}{20}
=-\sqrt{31}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{31}}{2*10}=\frac{0+20\sqrt{31}}{20}
=\frac{20\sqrt{31}}{20}
=\sqrt{31}
$