4x^2-12x-66=0

Solution for 4x^2-12x-66=0 equation:

4x^2-12x-66=0

a = 4; b = -12; c = -66;
Δ = b2-4ac
Δ = -122-4·4·(-66)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-20\sqrt{3}}{2*4}=\frac{12-20\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+20\sqrt{3}}{2*4}=\frac{12+20\sqrt{3}}{8}
$