6x^2-6x-75=0

Solution for 6x^2-6x-75=0 equation:

6x^2-6x-75=0

a = 6; b = -6; c = -75;
Δ = b2-4ac
Δ = -62-4·6·(-75)
Δ = 1836
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:

$\sqrt{\Delta}=\sqrt{1836}=\sqrt{36*51}=\sqrt{36}*\sqrt{51}=6\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{51}}{2*6}=\frac{6-6\sqrt{51}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{51}}{2*6}=\frac{6+6\sqrt{51}}{12}
$