12x^2-5=31

Solution for 12x^2-5=31 equation:

12x^2-5=31

We move all terms to the left:

12x^2-5-(31)=0

We add all the numbers together, and all the variables

12x^2-36=0

a = 12; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·12·(-36)
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{3}}{2*12}=\frac{0-24\sqrt{3}}{24}
=-\frac{24\sqrt{3}}{24}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{3}}{2*12}=\frac{0+24\sqrt{3}}{24}
=\frac{24\sqrt{3}}{24}
=\sqrt{3}
$