6x^2-12x-52=0

Solution for 6x^2-12x-52=0 equation:

6x^2-12x-52=0

a = 6; b = -12; c = -52;
Δ = b2-4ac
Δ = -122-4·6·(-52)
Δ = 1392
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:

$\sqrt{\Delta}=\sqrt{1392}=\sqrt{16*87}=\sqrt{16}*\sqrt{87}=4\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{87}}{2*6}=\frac{12-4\sqrt{87}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{87}}{2*6}=\frac{12+4\sqrt{87}}{12}
$