2(x^2-2x-66)=0

Solution for 2(x^2-2x-66)=0 equation:

2(x^2-2x-66)=0

We multiply parentheses

2x^2-4x-132=0

a = 2; b = -4; c = -132;
Δ = b2-4ac
Δ = -42-4·2·(-132)
Δ = 1072
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:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{67}}{2*2}=\frac{4-4\sqrt{67}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{67}}{2*2}=\frac{4+4\sqrt{67}}{4}
$