6x^2-12x-25=0

Solution for 6x^2-12x-25=0 equation:

6x^2-12x-25=0

a = 6; b = -12; c = -25;
Δ = b2-4ac
Δ = -122-4·6·(-25)
Δ = 744
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:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{186}}{2*6}=\frac{12-2\sqrt{186}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{186}}{2*6}=\frac{12+2\sqrt{186}}{12}
$