12x^2-44x-105=0

Solution for 12x^2-44x-105=0 equation:

12x^2-44x-105=0

a = 12; b = -44; c = -105;
Δ = b2-4ac
Δ = -442-4·12·(-105)
Δ = 6976
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:

$\sqrt{\Delta}=\sqrt{6976}=\sqrt{64*109}=\sqrt{64}*\sqrt{109}=8\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-8\sqrt{109}}{2*12}=\frac{44-8\sqrt{109}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+8\sqrt{109}}{2*12}=\frac{44+8\sqrt{109}}{24}
$