6x^2-2x-52=0

Solution for 6x^2-2x-52=0 equation:

6x^2-2x-52=0

a = 6; b = -2; c = -52;
Δ = b2-4ac
Δ = -22-4·6·(-52)
Δ = 1252
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:

$\sqrt{\Delta}=\sqrt{1252}=\sqrt{4*313}=\sqrt{4}*\sqrt{313}=2\sqrt{313}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{313}}{2*6}=\frac{2-2\sqrt{313}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{313}}{2*6}=\frac{2+2\sqrt{313}}{12}
$