12x^2-31+7=0

Solution for 12x^2-31+7=0 equation:

12x^2-31+7=0

We add all the numbers together, and all the variables

12x^2-24=0

a = 12; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·12·(-24)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*12}=\frac{0-24\sqrt{2}}{24}
=-\frac{24\sqrt{2}}{24}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*12}=\frac{0+24\sqrt{2}}{24}
=\frac{24\sqrt{2}}{24}
=\sqrt{2}
$