12x^2-44x-75=0

Solution for 12x^2-44x-75=0 equation:

12x^2-44x-75=0

a = 12; b = -44; c = -75;
Δ = b2-4ac
Δ = -442-4·12·(-75)
Δ = 5536
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:

$\sqrt{\Delta}=\sqrt{5536}=\sqrt{16*346}=\sqrt{16}*\sqrt{346}=4\sqrt{346}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{346}}{2*12}=\frac{44-4\sqrt{346}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{346}}{2*12}=\frac{44+4\sqrt{346}}{24}
$