12x^2-16x-300=0

Solution for 12x^2-16x-300=0 equation:

12x^2-16x-300=0

a = 12; b = -16; c = -300;
Δ = b2-4ac
Δ = -162-4·12·(-300)
Δ = 14656
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:

$\sqrt{\Delta}=\sqrt{14656}=\sqrt{64*229}=\sqrt{64}*\sqrt{229}=8\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{229}}{2*12}=\frac{16-8\sqrt{229}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{229}}{2*12}=\frac{16+8\sqrt{229}}{24}
$