12x^2-12x-1296=0

Solution for 12x^2-12x-1296=0 equation:

12x^2-12x-1296=0

a = 12; b = -12; c = -1296;
Δ = b2-4ac
Δ = -122-4·12·(-1296)
Δ = 62352
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:

$\sqrt{\Delta}=\sqrt{62352}=\sqrt{144*433}=\sqrt{144}*\sqrt{433}=12\sqrt{433}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{433}}{2*12}=\frac{12-12\sqrt{433}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{433}}{2*12}=\frac{12+12\sqrt{433}}{24}
$