6x^2+2=52

Solution for 6x^2+2=52 equation:

6x^2+2=52

We move all terms to the left:

6x^2+2-(52)=0

We add all the numbers together, and all the variables

6x^2-50=0

a = 6; b = 0; c = -50;
Δ = b2-4ac
Δ = 02-4·6·(-50)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{3}}{2*6}=\frac{0-20\sqrt{3}}{12}
=-\frac{20\sqrt{3}}{12}
=-\frac{5\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{3}}{2*6}=\frac{0+20\sqrt{3}}{12}
=\frac{20\sqrt{3}}{12}
=\frac{5\sqrt{3}}{3}
$