6x^2-66x-35=0

Solution for 6x^2-66x-35=0 equation:

6x^2-66x-35=0

a = 6; b = -66; c = -35;
Δ = b2-4ac
Δ = -662-4·6·(-35)
Δ = 5196
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:

$\sqrt{\Delta}=\sqrt{5196}=\sqrt{4*1299}=\sqrt{4}*\sqrt{1299}=2\sqrt{1299}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1299}}{2*6}=\frac{66-2\sqrt{1299}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1299}}{2*6}=\frac{66+2\sqrt{1299}}{12}
$